Algebra Examples

${(14 x^{2})}^{- 4} {(3 x)}^{4} {(13 x^{6})}^{2}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(14 x^{2})}^{4}} {(3 x)}^{4} {(13 x^{6})}^{2}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $14 x^{2}$ .

$\frac{1}{14^{4} {(x^{2})}^{4}} {(3 x)}^{4} {(13 x^{6})}^{2}$

Step 2.2

Raise $14$ to the power of $4$ .

$\frac{1}{38416 {(x^{2})}^{4}} {(3 x)}^{4} {(13 x^{6})}^{2}$

Step 2.3

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 2.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{38416 x^{2 \cdot 4}} {(3 x)}^{4} {(13 x^{6})}^{2}$

Step 2.3.2

Multiply $2$ by $4$ .

$\frac{1}{38416 x^{8}} {(3 x)}^{4} {(13 x^{6})}^{2}$

Step 3

Simplify terms.

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Step 3.1

Apply the product rule to $3 x$ .

$\frac{1}{38416 x^{8}} (3^{4} x^{4}) {(13 x^{6})}^{2}$

Step 3.2

Simplify the expression.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$3^{4} \frac{1}{38416 x^{8}} x^{4} {(13 x^{6})}^{2}$

Step 3.2.2

Raise $3$ to the power of $4$ .

$81 \frac{1}{38416 x^{8}} x^{4} {(13 x^{6})}^{2}$

Step 3.3

Combine $81$ and $\frac{1}{38416 x^{8}}$ .

$\frac{81}{38416 x^{8}} x^{4} {(13 x^{6})}^{2}$

Step 3.4

Cancel the common factor of $x^{4}$ .

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Step 3.4.1

Factor $x^{4}$ out of $38416 x^{8}$ .

$\frac{81}{x^{4} (38416 x^{4})} x^{4} {(13 x^{6})}^{2}$

Step 3.4.2

Cancel the common factor.

$\frac{81}{x^{4} (38416 x^{4})} x^{4} {(13 x^{6})}^{2}$

Step 3.4.3

Rewrite the expression.

$\frac{81}{38416 x^{4}} {(13 x^{6})}^{2}$

Step 3.5

Simplify the expression.

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Step 3.5.1

Apply the product rule to $13 x^{6}$ .

$\frac{81}{38416 x^{4}} (13^{2} {(x^{6})}^{2})$

Step 3.5.2

Rewrite using the commutative property of multiplication.

$13^{2} \frac{81}{38416 x^{4}} {(x^{6})}^{2}$

Step 3.5.3

Raise $13$ to the power of $2$ .

$169 \frac{81}{38416 x^{4}} {(x^{6})}^{2}$

Step 4

Multiply $169 \frac{81}{38416 x^{4}}$ .

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Step 4.1

Combine $169$ and $\frac{81}{38416 x^{4}}$ .

$\frac{169 \cdot 81}{38416 x^{4}} {(x^{6})}^{2}$

Step 4.2

Multiply $169$ by $81$ .

$\frac{13689}{38416 x^{4}} {(x^{6})}^{2}$

Step 5

Multiply the exponents in ${(x^{6})}^{2}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{13689}{38416 x^{4}} x^{6 \cdot 2}$

Step 5.2

Multiply $6$ by $2$ .

$\frac{13689}{38416 x^{4}} x^{12}$

Step 6

Cancel the common factor of $x^{4}$ .

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Step 6.1

Factor $x^{4}$ out of $38416 x^{4}$ .

$\frac{13689}{x^{4} \cdot 38416} x^{12}$

Step 6.2

Factor $x^{4}$ out of $x^{12}$ .

$\frac{13689}{x^{4} \cdot 38416} (x^{4} x^{8})$

Step 6.3

Cancel the common factor.

$\frac{13689}{x^{4} \cdot 38416} (x^{4} x^{8})$

Step 6.4

Rewrite the expression.

$\frac{13689}{38416} x^{8}$

Step 7

Combine $\frac{13689}{38416}$ and $x^{8}$ .

$\frac{13689 x^{8}}{38416}$