代数示例

$f (x) = \frac{x^{\frac{1}{5}}}{9} + 7$

解题步骤 1

将 $f (x) = \frac{x^{\frac{1}{5}}}{9} + 7$ 写为等式。

$y = \frac{x^{\frac{1}{5}}}{9} + 7$

解题步骤 2

交换变量。

$x = \frac{y^{\frac{1}{5}}}{9} + 7$

解题步骤 3

求解 $y$ 。

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解题步骤 3.1

将方程重写为 $\frac{y^{\frac{1}{5}}}{9} + 7 = x$ 。

$\frac{y^{\frac{1}{5}}}{9} + 7 = x$

解题步骤 3.2

将所有不包含 $y$ 的项移到等式右边。

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解题步骤 3.2.1

从等式两边同时减去 $7$ 。

$\frac{y^{\frac{1}{5}}}{9} - x = - 7$

解题步骤 3.2.2

在等式两边都加上 $x$ 。

$\frac{y^{\frac{1}{5}}}{9} = - 7 + x$

解题步骤 3.3

等式两边同时乘以 $9$ 。

$9 \frac{y^{\frac{1}{5}}}{9} = 9 (- 7 + x)$

解题步骤 3.4

化简方程的两边。

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解题步骤 3.4.1

化简左边。

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解题步骤 3.4.1.1

约去 $9$ 的公因数。

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解题步骤 3.4.1.1.1

约去公因数。

$9 \frac{y^{\frac{1}{5}}}{9} = 9 (- 7 + x)$

解题步骤 3.4.1.1.2

重写表达式。

$y^{\frac{1}{5}} = 9 (- 7 + x)$

解题步骤 3.4.2

化简右边。

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解题步骤 3.4.2.1

化简 $9 (- 7 + x)$ 。

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解题步骤 3.4.2.1.1

运用分配律。

$y^{\frac{1}{5}} = 9 \cdot - 7 + 9 x$

解题步骤 3.4.2.1.2

将 $9$ 乘以 $- 7$ 。

$y^{\frac{1}{5}} = - 63 + 9 x$

解题步骤 3.5

将方程两边同时进行 $5$ 次方运算以消去左边的分数指数。

${(y^{\frac{1}{5}})}^{5} = {(- 63 + 9 x)}^{5}$

解题步骤 3.6

化简指数。

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解题步骤 3.6.1

化简左边。

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解题步骤 3.6.1.1

化简 ${(y^{\frac{1}{5}})}^{5}$ 。

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解题步骤 3.6.1.1.1

将 ${(y^{\frac{1}{5}})}^{5}$ 中的指数相乘。

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解题步骤 3.6.1.1.1.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$y^{\frac{1}{5} \cdot 5} = {(- 63 + 9 x)}^{5}$

解题步骤 3.6.1.1.1.2

约去 $5$ 的公因数。

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解题步骤 3.6.1.1.1.2.1

约去公因数。

$y^{\frac{1}{5} \cdot 5} = {(- 63 + 9 x)}^{5}$

解题步骤 3.6.1.1.1.2.2

重写表达式。

$y^{1} = {(- 63 + 9 x)}^{5}$

解题步骤 3.6.1.1.2

化简。

$y = {(- 63 + 9 x)}^{5}$

解题步骤 3.6.2

化简右边。

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解题步骤 3.6.2.1

化简 ${(- 63 + 9 x)}^{5}$ 。

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解题步骤 3.6.2.1.1

使用二项式定理。

$y = {(- 63)}^{5} + 5 {(- 63)}^{4} (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2

化简每一项。

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解题步骤 3.6.2.1.2.1

对 $- 63$ 进行 $5$ 次方运算。

$y = - 992436543 + 5 {(- 63)}^{4} (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.2

对 $- 63$ 进行 $4$ 次方运算。

$y = - 992436543 + 5 \cdot 15752961 (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.3

将 $5$ 乘以 $15752961$ 。

$y = - 992436543 + 78764805 (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.4

将 $9$ 乘以 $78764805$ 。

$y = - 992436543 + 708883245 x + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.5

对 $- 63$ 进行 $3$ 次方运算。

$y = - 992436543 + 708883245 x + 10 \cdot - 250047 {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.6

将 $10$ 乘以 $- 250047$ 。

$y = - 992436543 + 708883245 x - 2500470 {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.7

对 $9 x$ 运用乘积法则。

$y = - 992436543 + 708883245 x - 2500470 (9^{2} x^{2}) + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.8

对 $9$ 进行 $2$ 次方运算。

$y = - 992436543 + 708883245 x - 2500470 (81 x^{2}) + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.9

将 $81$ 乘以 $- 2500470$ 。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.10

对 $- 63$ 进行 $2$ 次方运算。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 10 \cdot 3969 {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.11

将 $10$ 乘以 $3969$ 。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 39690 {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.12

对 $9 x$ 运用乘积法则。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 39690 (9^{3} x^{3}) + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.13

对 $9$ 进行 $3$ 次方运算。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 39690 (729 x^{3}) + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.14

将 $729$ 乘以 $39690$ 。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.15

将 $5$ 乘以 $- 63$ 。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 315 {(9 x)}^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.16

对 $9 x$ 运用乘积法则。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 315 (9^{4} x^{4}) + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.17

对 $9$ 进行 $4$ 次方运算。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 315 (6561 x^{4}) + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.18

将 $6561$ 乘以 $- 315$ 。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + {(9 x)}^{5}$

解题步骤 3.6.2.1.2.19

对 $9 x$ 运用乘积法则。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 9^{5} x^{5}$

解题步骤 3.6.2.1.2.20

对 $9$ 进行 $5$ 次方运算。

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5}$

解题步骤 3.7

化简 $- 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5}$ 。

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解题步骤 3.7.1

移动 $- 992436543$ 。

$y = 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5} - 992436543$

解题步骤 3.7.2

移动 $708883245 x$ 。

$y = - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5} + 708883245 x - 992436543$

解题步骤 3.7.3

移动 $- 202538070 x^{2}$ 。

$y = 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5} - 202538070 x^{2} + 708883245 x - 992436543$

解题步骤 3.7.4

移动 $28934010 x^{3}$ 。

$y = - 2066715 x^{4} + 59049 x^{5} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

解题步骤 3.7.5

将 $- 2066715 x^{4}$ 和 $59049 x^{5}$ 重新排序。

$y = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

解题步骤 4

使用 $f^{- 1} (x)$ 替换 $y$ ，以得到最终答案。

$f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

解题步骤 5

验证 $f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$ 是否为 $f (x) = \frac{x^{\frac{1}{5}}}{9} + 7$ 的反函数。

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解题步骤 5.1

要验证反函数，请检查 $f^{- 1} (f (x)) = x$ 和 $f (f^{- 1} (x)) = x$ 是否成立。

解题步骤 5.2

计算 $f^{- 1} (f (x))$ 。

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解题步骤 5.2.1

建立复合结果函数。

$f^{- 1} (f (x))$

解题步骤 5.2.2

通过将 $f$ 的值代入 $f^{- 1}$ 来计算 $f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7)$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{5} - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3

化简每一项。

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解题步骤 5.2.3.1

使用二项式定理。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 ({(\frac{x^{\frac{1}{5}}}{9})}^{5} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2

化简每一项。

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解题步骤 5.2.3.2.1

对 $\frac{x^{\frac{1}{5}}}{9}$ 运用乘积法则。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{{(x^{\frac{1}{5}})}^{5}}{9^{5}} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.2

化简分子。

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解题步骤 5.2.3.2.2.1

将 ${(x^{\frac{1}{5}})}^{5}$ 中的指数相乘。

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解题步骤 5.2.3.2.2.1.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x^{\frac{1}{5} \cdot 5}}{9^{5}} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.2.1.2

约去 $5$ 的公因数。

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解题步骤 5.2.3.2.2.1.2.1

约去公因数。

解题步骤 5.2.3.2.2.1.2.2

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{9^{5}} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.2.2

化简。

解题步骤 5.2.3.2.3

对 $9$ 进行 $5$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.4

对 $\frac{x^{\frac{1}{5}}}{9}$ 运用乘积法则。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{{(x^{\frac{1}{5}})}^{4}}{9^{4}}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.5

将 ${(x^{\frac{1}{5}})}^{4}$ 中的指数相乘。

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解题步骤 5.2.3.2.5.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{x^{\frac{1}{5} \cdot 4}}{9^{4}}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.5.2

组合 $\frac{1}{5}$ 和 $4$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{x^{\frac{4}{5}}}{9^{4}}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.6

对 $9$ 进行 $4$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{x^{\frac{4}{5}}}{6561}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.7

组合 $5$ 和 $\frac{x^{\frac{4}{5}}}{6561}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{5 x^{\frac{4}{5}}}{6561} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.8

乘以 $\frac{5 x^{\frac{4}{5}}}{6561} \cdot 7$ 。

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解题步骤 5.2.3.2.8.1

组合 $\frac{5 x^{\frac{4}{5}}}{6561}$ 和 $7$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{5 x^{\frac{4}{5}} \cdot 7}{6561} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.8.2

将 $7$ 乘以 $5$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.9

对 $\frac{x^{\frac{1}{5}}}{9}$ 运用乘积法则。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{{(x^{\frac{1}{5}})}^{3}}{9^{3}}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.10

将 ${(x^{\frac{1}{5}})}^{3}$ 中的指数相乘。

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解题步骤 5.2.3.2.10.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{x^{\frac{1}{5} \cdot 3}}{9^{3}}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.10.2

组合 $\frac{1}{5}$ 和 $3$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{x^{\frac{3}{5}}}{9^{3}}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.11

对 $9$ 进行 $3$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{x^{\frac{3}{5}}}{729}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.12

组合 $10$ 和 $\frac{x^{\frac{3}{5}}}{729}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{10 x^{\frac{3}{5}}}{729} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.13

对 $7$ 进行 $2$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{10 x^{\frac{3}{5}}}{729} \cdot 49 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.14

乘以 $\frac{10 x^{\frac{3}{5}}}{729} \cdot 49$ 。

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解题步骤 5.2.3.2.14.1

组合 $\frac{10 x^{\frac{3}{5}}}{729}$ 和 $49$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{10 x^{\frac{3}{5}} \cdot 49}{729} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.14.2

将 $49$ 乘以 $10$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.15

对 $\frac{x^{\frac{1}{5}}}{9}$ 运用乘积法则。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{{(x^{\frac{1}{5}})}^{2}}{9^{2}}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.16

将 ${(x^{\frac{1}{5}})}^{2}$ 中的指数相乘。

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解题步骤 5.2.3.2.16.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{x^{\frac{1}{5} \cdot 2}}{9^{2}}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.16.2

组合 $\frac{1}{5}$ 和 $2$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{x^{\frac{2}{5}}}{9^{2}}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.17

对 $9$ 进行 $2$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{x^{\frac{2}{5}}}{81}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.18

组合 $10$ 和 $\frac{x^{\frac{2}{5}}}{81}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{10 x^{\frac{2}{5}}}{81} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.19

对 $7$ 进行 $3$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{10 x^{\frac{2}{5}}}{81} \cdot 343 + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.20

乘以 $\frac{10 x^{\frac{2}{5}}}{81} \cdot 343$ 。

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解题步骤 5.2.3.2.20.1

组合 $\frac{10 x^{\frac{2}{5}}}{81}$ 和 $343$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{10 x^{\frac{2}{5}} \cdot 343}{81} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.20.2

将 $343$ 乘以 $10$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.21

组合 $5$ 和 $\frac{x^{\frac{1}{5}}}{9}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{5 x^{\frac{1}{5}}}{9} \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.22

对 $7$ 进行 $4$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{5 x^{\frac{1}{5}}}{9} \cdot 2401 + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.23

乘以 $\frac{5 x^{\frac{1}{5}}}{9} \cdot 2401$ 。

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解题步骤 5.2.3.2.23.1

组合 $\frac{5 x^{\frac{1}{5}}}{9}$ 和 $2401$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{5 x^{\frac{1}{5}} \cdot 2401}{9} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.23.2

将 $2401$ 乘以 $5$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{12005 x^{\frac{1}{5}}}{9} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.2.24

对 $7$ 进行 $5$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{12005 x^{\frac{1}{5}}}{9} + 16807) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.3

运用分配律。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049}) + 59049 (\frac{35 x^{\frac{4}{5}}}{6561}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4

化简。

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解题步骤 5.2.3.4.1

约去 $59049$ 的公因数。

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解题步骤 5.2.3.4.1.1

约去公因数。

解题步骤 5.2.3.4.1.2

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 59049 (\frac{35 x^{\frac{4}{5}}}{6561}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.2

约去 $6561$ 的公因数。

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解题步骤 5.2.3.4.2.1

从 $59049$ 中分解出因数 $6561$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 6561 (9) (\frac{35 x^{\frac{4}{5}}}{6561}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.2.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 6561 \cdot (9 (\frac{35 x^{\frac{4}{5}}}{6561})) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.2.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 9 (35 x^{\frac{4}{5}}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.3

将 $35$ 乘以 $9$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.4

约去 $729$ 的公因数。

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解题步骤 5.2.3.4.4.1

从 $59049$ 中分解出因数 $729$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 729 (81) (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.4.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 729 \cdot (81 (\frac{490 x^{\frac{3}{5}}}{729})) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.4.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 81 (490 x^{\frac{3}{5}}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.5

将 $490$ 乘以 $81$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.6

约去 $81$ 的公因数。

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解题步骤 5.2.3.4.6.1

从 $59049$ 中分解出因数 $81$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 81 (729) (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.6.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 81 \cdot (729 (\frac{3430 x^{\frac{2}{5}}}{81})) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.6.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 729 (3430 x^{\frac{2}{5}}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.7

将 $3430$ 乘以 $729$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.8

约去 $9$ 的公因数。

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解题步骤 5.2.3.4.8.1

从 $59049$ 中分解出因数 $9$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 9 (6561) (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.8.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 9 \cdot (6561 (\frac{12005 x^{\frac{1}{5}}}{9})) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.8.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 6561 (12005 x^{\frac{1}{5}}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.9

将 $12005$ 乘以 $6561$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.4.10

将 $59049$ 乘以 $16807$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.5

使用二项式定理。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 ({(\frac{x^{\frac{1}{5}}}{9})}^{4} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6

化简每一项。

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解题步骤 5.2.3.6.1

对 $\frac{x^{\frac{1}{5}}}{9}$ 运用乘积法则。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{{(x^{\frac{1}{5}})}^{4}}{9^{4}} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.2

将 ${(x^{\frac{1}{5}})}^{4}$ 中的指数相乘。

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解题步骤 5.2.3.6.2.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{1}{5} \cdot 4}}{9^{4}} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.2.2

组合 $\frac{1}{5}$ 和 $4$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{9^{4}} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.3

对 $9$ 进行 $4$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.4

对 $\frac{x^{\frac{1}{5}}}{9}$ 运用乘积法则。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{{(x^{\frac{1}{5}})}^{3}}{9^{3}}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.5

将 ${(x^{\frac{1}{5}})}^{3}$ 中的指数相乘。

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解题步骤 5.2.3.6.5.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{x^{\frac{1}{5} \cdot 3}}{9^{3}}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.5.2

组合 $\frac{1}{5}$ 和 $3$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{x^{\frac{3}{5}}}{9^{3}}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.6

对 $9$ 进行 $3$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{x^{\frac{3}{5}}}{729}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.7

组合 $4$ 和 $\frac{x^{\frac{3}{5}}}{729}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{4 x^{\frac{3}{5}}}{729} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.8

乘以 $\frac{4 x^{\frac{3}{5}}}{729} \cdot 7$ 。

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解题步骤 5.2.3.6.8.1

组合 $\frac{4 x^{\frac{3}{5}}}{729}$ 和 $7$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{4 x^{\frac{3}{5}} \cdot 7}{729} + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.8.2

将 $7$ 乘以 $4$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.9

对 $\frac{x^{\frac{1}{5}}}{9}$ 运用乘积法则。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{{(x^{\frac{1}{5}})}^{2}}{9^{2}}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.10

将 ${(x^{\frac{1}{5}})}^{2}$ 中的指数相乘。

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解题步骤 5.2.3.6.10.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{x^{\frac{1}{5} \cdot 2}}{9^{2}}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.10.2

组合 $\frac{1}{5}$ 和 $2$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{x^{\frac{2}{5}}}{9^{2}}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.11

对 $9$ 进行 $2$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{x^{\frac{2}{5}}}{81}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.12

约去 $3$ 的公因数。

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解题步骤 5.2.3.6.12.1

从 $6$ 中分解出因数 $3$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 3 (2) (\frac{x^{\frac{2}{5}}}{81}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.12.2

从 $81$ 中分解出因数 $3$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 3 \cdot (2 (\frac{x^{\frac{2}{5}}}{3 \cdot 27})) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.12.3

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 3 \cdot (2 (\frac{x^{\frac{2}{5}}}{3 \cdot 27})) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.12.4

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 2 (\frac{x^{\frac{2}{5}}}{27}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.13

组合 $2$ 和 $\frac{x^{\frac{2}{5}}}{27}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{2 x^{\frac{2}{5}}}{27} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.14

对 $7$ 进行 $2$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{2 x^{\frac{2}{5}}}{27} \cdot 49 + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.15

乘以 $\frac{2 x^{\frac{2}{5}}}{27} \cdot 49$ 。

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解题步骤 5.2.3.6.15.1

组合 $\frac{2 x^{\frac{2}{5}}}{27}$ 和 $49$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{2 x^{\frac{2}{5}} \cdot 49}{27} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.15.2

将 $49$ 乘以 $2$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.16

组合 $4$ 和 $\frac{x^{\frac{1}{5}}}{9}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{4 x^{\frac{1}{5}}}{9} \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.17

对 $7$ 进行 $3$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{4 x^{\frac{1}{5}}}{9} \cdot 343 + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.18

乘以 $\frac{4 x^{\frac{1}{5}}}{9} \cdot 343$ 。

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解题步骤 5.2.3.6.18.1

组合 $\frac{4 x^{\frac{1}{5}}}{9}$ 和 $343$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{4 x^{\frac{1}{5}} \cdot 343}{9} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.18.2

将 $343$ 乘以 $4$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{1372 x^{\frac{1}{5}}}{9} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.6.19

对 $7$ 进行 $4$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{1372 x^{\frac{1}{5}}}{9} + 2401) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.7

运用分配律。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 \frac{x^{\frac{4}{5}}}{6561} - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8

化简。

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解题步骤 5.2.3.8.1

约去 $6561$ 的公因数。

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解题步骤 5.2.3.8.1.1

从 $- 2066715$ 中分解出因数 $6561$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 + 6561 (- 315) (\frac{x^{\frac{4}{5}}}{6561}) - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.1.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 + 6561 \cdot (- 315 \frac{x^{\frac{4}{5}}}{6561}) - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.1.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.2

约去 $729$ 的公因数。

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解题步骤 5.2.3.8.2.1

从 $- 2066715$ 中分解出因数 $729$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} + 729 (- 2835) (\frac{28 x^{\frac{3}{5}}}{729}) - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.2.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} + 729 \cdot (- 2835 \frac{28 x^{\frac{3}{5}}}{729}) - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.2.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 2835 (28 x^{\frac{3}{5}}) - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.3

将 $28$ 乘以 $- 2835$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.4

约去 $27$ 的公因数。

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解题步骤 5.2.3.8.4.1

从 $- 2066715$ 中分解出因数 $27$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} + 27 (- 76545) (\frac{98 x^{\frac{2}{5}}}{27}) - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.4.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} + 27 \cdot (- 76545 \frac{98 x^{\frac{2}{5}}}{27}) - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.4.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 76545 (98 x^{\frac{2}{5}}) - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.5

将 $98$ 乘以 $- 76545$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.6

约去 $9$ 的公因数。

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解题步骤 5.2.3.8.6.1

从 $- 2066715$ 中分解出因数 $9$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} + 9 (- 229635) (\frac{1372 x^{\frac{1}{5}}}{9}) - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.6.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} + 9 \cdot (- 229635 \frac{1372 x^{\frac{1}{5}}}{9}) - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.6.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 229635 (1372 x^{\frac{1}{5}}) - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.7

将 $1372$ 乘以 $- 229635$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.8.8

将 $- 2066715$ 乘以 $2401$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.9

使用二项式定理。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 ({(\frac{x^{\frac{1}{5}}}{9})}^{3} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10

化简每一项。

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解题步骤 5.2.3.10.1

对 $\frac{x^{\frac{1}{5}}}{9}$ 运用乘积法则。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{{(x^{\frac{1}{5}})}^{3}}{9^{3}} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.2

将 ${(x^{\frac{1}{5}})}^{3}$ 中的指数相乘。

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解题步骤 5.2.3.10.2.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{1}{5} \cdot 3}}{9^{3}} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.2.2

组合 $\frac{1}{5}$ 和 $3$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{9^{3}} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.3

对 $9$ 进行 $3$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.4

对 $\frac{x^{\frac{1}{5}}}{9}$ 运用乘积法则。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{{(x^{\frac{1}{5}})}^{2}}{9^{2}}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.5

将 ${(x^{\frac{1}{5}})}^{2}$ 中的指数相乘。

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解题步骤 5.2.3.10.5.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{1}{5} \cdot 2}}{9^{2}}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.5.2

组合 $\frac{1}{5}$ 和 $2$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{9^{2}}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.6

对 $9$ 进行 $2$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{81}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.7

约去 $3$ 的公因数。

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解题步骤 5.2.3.10.7.1

从 $81$ 中分解出因数 $3$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{3 (27)}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.7.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{3 \cdot 27}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.7.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{x^{\frac{2}{5}}}{27} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.8

组合 $\frac{x^{\frac{2}{5}}}{27}$ 和 $7$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{x^{\frac{2}{5}} \cdot 7}{27} + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.9

将 $7$ 移到 $x^{\frac{2}{5}}$ 的左侧。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 \cdot x^{\frac{2}{5}}}{27} + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.10

约去 $3$ 的公因数。

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解题步骤 5.2.3.10.10.1

从 $9$ 中分解出因数 $3$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + 3 (\frac{x^{\frac{1}{5}}}{3 (3)}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.10.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + 3 (\frac{x^{\frac{1}{5}}}{3 \cdot 3}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.10.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{x^{\frac{1}{5}}}{3} \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.11

对 $7$ 进行 $2$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{x^{\frac{1}{5}}}{3} \cdot 49 + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.12

组合 $\frac{x^{\frac{1}{5}}}{3}$ 和 $49$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{x^{\frac{1}{5}} \cdot 49}{3} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.13

将 $49$ 移到 $x^{\frac{1}{5}}$ 的左侧。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{49 \cdot x^{\frac{1}{5}}}{3} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.10.14

对 $7$ 进行 $3$ 次方运算。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{49 x^{\frac{1}{5}}}{3} + 343) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.11

运用分配律。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729}) + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12

化简。

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解题步骤 5.2.3.12.1

约去 $729$ 的公因数。

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解题步骤 5.2.3.12.1.1

从 $28934010$ 中分解出因数 $729$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 729 (39690) (\frac{x^{\frac{3}{5}}}{729}) + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.1.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 729 \cdot (39690 (\frac{x^{\frac{3}{5}}}{729})) + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.1.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.2

约去 $27$ 的公因数。

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解题步骤 5.2.3.12.2.1

从 $28934010$ 中分解出因数 $27$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 27 (1071630) (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.2.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 27 \cdot (1071630 (\frac{7 x^{\frac{2}{5}}}{27})) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.2.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 1071630 (7 x^{\frac{2}{5}}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.3

将 $7$ 乘以 $1071630$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.4

约去 $3$ 的公因数。

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解题步骤 5.2.3.12.4.1

从 $28934010$ 中分解出因数 $3$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 3 (9644670) (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.4.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 3 \cdot (9644670 (\frac{49 x^{\frac{1}{5}}}{3})) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.4.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 9644670 (49 x^{\frac{1}{5}}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.5

将 $49$ 乘以 $9644670$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.12.6

将 $28934010$ 乘以 $343$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.13

将 ${(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2}$ 重写为 $(\frac{x^{\frac{1}{5}}}{9} + 7) (\frac{x^{\frac{1}{5}}}{9} + 7)$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 ((\frac{x^{\frac{1}{5}}}{9} + 7) (\frac{x^{\frac{1}{5}}}{9} + 7)) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.14

使用 FOIL 方法展开 $(\frac{x^{\frac{1}{5}}}{9} + 7) (\frac{x^{\frac{1}{5}}}{9} + 7)$ 。

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解题步骤 5.2.3.14.1

运用分配律。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}}}{9} \cdot (\frac{x^{\frac{1}{5}}}{9} + 7) + 7 (\frac{x^{\frac{1}{5}}}{9} + 7)) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.14.2

运用分配律。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}}}{9} \cdot \frac{x^{\frac{1}{5}}}{9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9} + 7)) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.14.3

运用分配律。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}}}{9} \cdot \frac{x^{\frac{1}{5}}}{9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.15

化简并合并同类项。

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解题步骤 5.2.3.15.1

化简每一项。

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解题步骤 5.2.3.15.1.1

合并。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}} x^{\frac{1}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.15.1.2

通过指数相加将 $x^{\frac{1}{5}}$ 乘以 $x^{\frac{1}{5}}$ 。

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解题步骤 5.2.3.15.1.2.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5} + \frac{1}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.15.1.2.2

在公分母上合并分子。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1 + 1}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.15.1.2.3

将 $1$ 和 $1$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.15.1.3

将 $9$ 乘以 $9$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.15.1.4

组合 $\frac{x^{\frac{1}{5}}}{9}$ 和 $7$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{x^{\frac{1}{5}} \cdot 7}{9} + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.15.1.5

将 $7$ 移到 $x^{\frac{1}{5}}$ 的左侧。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{7 \cdot x^{\frac{1}{5}}}{9} + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.15.1.6

组合 $7$ 和 $\frac{x^{\frac{1}{5}}}{9}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{7 x^{\frac{1}{5}}}{9} + \frac{7 x^{\frac{1}{5}}}{9} + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.15.1.7

将 $7$ 乘以 $7$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{7 x^{\frac{1}{5}}}{9} + \frac{7 x^{\frac{1}{5}}}{9} + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.15.2

将 $\frac{7 x^{\frac{1}{5}}}{9}$ 和 $\frac{7 x^{\frac{1}{5}}}{9}$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + 2 (\frac{7 x^{\frac{1}{5}}}{9}) + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.16

乘以 $2 \frac{7 x^{\frac{1}{5}}}{9}$ 。

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解题步骤 5.2.3.16.1

组合 $2$ 和 $\frac{7 x^{\frac{1}{5}}}{9}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{2 (7 x^{\frac{1}{5}})}{9} + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.16.2

将 $7$ 乘以 $2$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{14 x^{\frac{1}{5}}}{9} + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.17

运用分配律。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 \frac{x^{\frac{2}{5}}}{81} - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.18

化简。

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解题步骤 5.2.3.18.1

约去 $81$ 的公因数。

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解题步骤 5.2.3.18.1.1

从 $- 202538070$ 中分解出因数 $81$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 + 81 (- 2500470) (\frac{x^{\frac{2}{5}}}{81}) - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.18.1.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 + 81 \cdot (- 2500470 \frac{x^{\frac{2}{5}}}{81}) - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.18.1.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.18.2

约去 $9$ 的公因数。

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解题步骤 5.2.3.18.2.1

从 $- 202538070$ 中分解出因数 $9$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} + 9 (- 22504230) (\frac{14 x^{\frac{1}{5}}}{9}) - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.18.2.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} + 9 \cdot (- 22504230 \frac{14 x^{\frac{1}{5}}}{9}) - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.18.2.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 22504230 (14 x^{\frac{1}{5}}) - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.18.3

将 $14$ 乘以 $- 22504230$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.18.4

将 $- 202538070$ 乘以 $49$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

解题步骤 5.2.3.19

运用分配律。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 708883245 (\frac{x^{\frac{1}{5}}}{9}) + 708883245 \cdot 7 - 992436543$

解题步骤 5.2.3.20

约去 $9$ 的公因数。

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解题步骤 5.2.3.20.1

从 $708883245$ 中分解出因数 $9$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 9 (78764805) (\frac{x^{\frac{1}{5}}}{9}) + 708883245 \cdot 7 - 992436543$

解题步骤 5.2.3.20.2

约去公因数。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 9 \cdot (78764805 (\frac{x^{\frac{1}{5}}}{9})) + 708883245 \cdot 7 - 992436543$

解题步骤 5.2.3.20.3

重写表达式。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 708883245 \cdot 7 - 992436543$

解题步骤 5.2.3.21

将 $708883245$ 乘以 $7$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

解题步骤 5.2.4

通过加上各项进行化简。

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解题步骤 5.2.4.1

合并 $x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$ 中相反的项。

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解题步骤 5.2.4.1.1

从 $315 x^{\frac{4}{5}}$ 中减去 $315 x^{\frac{4}{5}}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 + 0 - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

解题步骤 5.2.4.1.2

将 $x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543$ 和 $0$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

解题步骤 5.2.4.1.3

将 $- 7501410 x^{\frac{2}{5}}$ 和 $7501410 x^{\frac{2}{5}}$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 0 + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

解题步骤 5.2.4.1.4

将 $x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}}$ 和 $0$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

解题步骤 5.2.4.1.5

从 $2500470 x^{\frac{2}{5}}$ 中减去 $2500470 x^{\frac{2}{5}}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 + 0 - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

解题步骤 5.2.4.1.6

将 $x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430$ 和 $0$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

解题步骤 5.2.4.1.7

从 $9924365430$ 中减去 $9924365430$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 0 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

解题步骤 5.2.4.1.8

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

解题步骤 5.2.4.1.9

将 $- 4962182715$ 和 $4962182715$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}} + 0 - 992436543$

解题步骤 5.2.4.1.10

将 $x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$ 和 $0$ 相加。

解题步骤 5.2.4.1.11

从 $992436543$ 中减去 $992436543$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}} + 0$

解题步骤 5.2.4.1.12

将 $x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$ 和 $0$ 相加。

解题步骤 5.2.4.2

从 $39690 x^{\frac{3}{5}}$ 中减去 $79380 x^{\frac{3}{5}}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 78764805 x^{\frac{1}{5}} - 39690 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

解题步骤 5.2.4.3

合并 $x + 78764805 x^{\frac{1}{5}} - 39690 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$ 中相反的项。

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解题步骤 5.2.4.3.1

将 $- 39690 x^{\frac{3}{5}}$ 和 $39690 x^{\frac{3}{5}}$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 78764805 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 0 + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

解题步骤 5.2.4.3.2

将 $x + 78764805 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}}$ 和 $0$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 78764805 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

解题步骤 5.2.4.4

从 $78764805 x^{\frac{1}{5}}$ 中减去 $315059220 x^{\frac{1}{5}}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x - 236294415 x^{\frac{1}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

解题步骤 5.2.4.5

将 $- 236294415 x^{\frac{1}{5}}$ 和 $472588830 x^{\frac{1}{5}}$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 236294415 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

解题步骤 5.2.4.6

从 $236294415 x^{\frac{1}{5}}$ 中减去 $315059220 x^{\frac{1}{5}}$ 。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x - 78764805 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

解题步骤 5.2.4.7

合并 $x - 78764805 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$ 中相反的项。

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解题步骤 5.2.4.7.1

将 $- 78764805 x^{\frac{1}{5}}$ 和 $78764805 x^{\frac{1}{5}}$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 0$

解题步骤 5.2.4.7.2

将 $x$ 和 $0$ 相加。

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x$

解题步骤 5.3

计算 $f (f^{- 1} (x))$ 。

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解题步骤 5.3.1

建立复合结果函数。

$f (f^{- 1} (x))$

解题步骤 5.3.2

通过将 $f^{- 1}$ 的值代入 $f$ 来计算 $f (59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543)$ 。

$f (59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543) = \frac{{(59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543)}^{\frac{1}{5}}}{9} + 7$

解题步骤 5.3.3

要将 $7$ 写成带有公分母的分数，请乘以 $\frac{9}{9}$ 。

解题步骤 5.3.4

组合 $7$ 和 $\frac{9}{9}$ 。

解题步骤 5.3.5

在公分母上合并分子。

解题步骤 5.3.6

将 $7$ 乘以 $9$ 。

解题步骤 5.4

由于 $f^{- 1} (f (x)) = x$ 和 $f (f^{- 1} (x)) = x$ ，因此 $f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$ 为 $f (x) = \frac{x^{\frac{1}{5}}}{9} + 7$ 的反函数。

$f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

代数 示例

代数示例