Algebra Examples

${(- 2 x y^{2})}^{5} (\frac{x^{7}}{8 y^{3}})$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

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

${(- 2 x)}^{5} {(y^{2})}^{5} \frac{x^{7}}{8 y^{3}}$

Step 1.2

Apply the product rule to $- 2 x$ .

${(- 2)}^{5} x^{5} {(y^{2})}^{5} \frac{x^{7}}{8 y^{3}}$

Step 2

Raise $- 2$ to the power of $5$ .

$- 32 x^{5} {(y^{2})}^{5} \frac{x^{7}}{8 y^{3}}$

Step 3

Cancel the common factor of $8$ .

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Step 3.1

Factor $8$ out of $- 32 x^{5} {(y^{2})}^{5}$ .

$8 (- 4 x^{5} {(y^{2})}^{5}) \frac{x^{7}}{8 y^{3}}$

Step 3.2

Factor $8$ out of $8 y^{3}$ .

$8 (- 4 x^{5} {(y^{2})}^{5}) \frac{x^{7}}{8 (y^{3})}$

Step 3.3

Cancel the common factor.

$8 (- 4 x^{5} {(y^{2})}^{5}) \frac{x^{7}}{8 y^{3}}$

Step 3.4

Rewrite the expression.

$- 4 x^{5} {(y^{2})}^{5} \frac{x^{7}}{y^{3}}$

Step 4

Combine $- 4$ and $\frac{x^{7}}{y^{3}}$ .

$x^{5} {(y^{2})}^{5} \frac{- 4 x^{7}}{y^{3}}$

Step 5

Combine $x^{5}$ and $\frac{- 4 x^{7}}{y^{3}}$ .

${(y^{2})}^{5} \frac{x^{5} (- 4 x^{7})}{y^{3}}$

Step 6

Multiply $x^{5}$ by $x^{7}$ by adding the exponents.

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Step 6.1

Move $x^{7}$ .

${(y^{2})}^{5} \frac{x^{7} x^{5} \cdot - 4}{y^{3}}$

Step 6.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(y^{2})}^{5} \frac{x^{7 + 5} \cdot - 4}{y^{3}}$

Step 6.3

Add $7$ and $5$ .

${(y^{2})}^{5} \frac{x^{12} \cdot - 4}{y^{3}}$

Step 7

Combine ${(y^{2})}^{5}$ and $\frac{x^{12} \cdot - 4}{y^{3}}$ .

$\frac{{(y^{2})}^{5} (x^{12} \cdot - 4)}{y^{3}}$

Step 8

Multiply the exponents in ${(y^{2})}^{5}$ .

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Step 8.1

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

$\frac{y^{2 \cdot 5} x^{12} \cdot - 4}{y^{3}}$

Step 8.2

Multiply $2$ by $5$ .

$\frac{y^{10} x^{12} \cdot - 4}{y^{3}}$

Step 9

Cancel the common factor of $y^{10}$ and $y^{3}$ .

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Step 9.1

Factor $y^{3}$ out of $y^{10} x^{12} \cdot - 4$ .

$\frac{y^{3} (y^{7} x^{12} \cdot - 4)}{y^{3}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Multiply by $1$ .

$\frac{y^{3} (y^{7} x^{12} \cdot - 4)}{y^{3} \cdot 1}$

Step 9.2.2

Cancel the common factor.

$\frac{y^{3} (y^{7} x^{12} \cdot - 4)}{y^{3} \cdot 1}$

Step 9.2.3

Rewrite the expression.

$\frac{y^{7} x^{12} \cdot - 4}{1}$

Step 9.2.4

Divide $y^{7} x^{12} \cdot - 4$ by $1$ .

$y^{7} x^{12} \cdot - 4$

Step 10

Move $- 4$ to the left of $y^{7} x^{12}$ .

$- 4 y^{7} x^{12}$