Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

Move ${(x^{- 5} y^{3})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(2 x^{- 2} y^{2})}^{- 3} {(x^{- 5} y^{3})}^{2}}$

Step 1.2

Move ${(2 x^{- 2} y^{2})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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

$\frac{{(2 \frac{1}{x^{2}})}^{3} {(y^{2})}^{3}}{{(x^{- 5} y^{3})}^{2}}$

Step 2.3

Combine $2$ and $\frac{1}{x^{2}}$ .

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

Step 2.4

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

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

Step 2.5

Raise $2$ to the power of $3$ .

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

Step 2.6

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 2.6.1

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

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

Step 2.6.2

Multiply $2$ by $3$ .

$\frac{\frac{8}{x^{6}} {(y^{2})}^{3}}{{(x^{- 5} y^{3})}^{2}}$

Step 2.7

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 2.7.1

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

$\frac{\frac{8}{x^{6}} y^{2 \cdot 3}}{{(x^{- 5} y^{3})}^{2}}$

Step 2.7.2

Multiply $2$ by $3$ .

$\frac{\frac{8}{x^{6}} y^{6}}{{(x^{- 5} y^{3})}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $x^{- 5} y^{3}$ .

$\frac{\frac{8}{x^{6}} y^{6}}{{(x^{- 5})}^{2} {(y^{3})}^{2}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{\frac{8}{x^{6}} y^{6}}{x^{- 5 \cdot 2} {(y^{3})}^{2}}$

Step 3.2.2

Multiply $- 5$ by $2$ .

$\frac{\frac{8}{x^{6}} y^{6}}{x^{- 10} {(y^{3})}^{2}}$

Step 3.3

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

$\frac{\frac{8}{x^{6}} y^{6}}{\frac{1}{x^{10}} {(y^{3})}^{2}}$

Step 3.4

Multiply the exponents in ${(y^{3})}^{2}$ .

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Step 3.4.1

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

$\frac{\frac{8}{x^{6}} y^{6}}{\frac{1}{x^{10}} y^{3 \cdot 2}}$

Step 3.4.2

Multiply $3$ by $2$ .

$\frac{\frac{8}{x^{6}} y^{6}}{\frac{1}{x^{10}} y^{6}}$

Step 4

Combine fractions.

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Step 4.1

Combine $\frac{8}{x^{6}}$ and $y^{6}$ .

$\frac{\frac{8 y^{6}}{x^{6}}}{\frac{1}{x^{10}} y^{6}}$

Step 4.2

Combine $\frac{1}{x^{10}}$ and $y^{6}$ .

$\frac{\frac{8 y^{6}}{x^{6}}}{\frac{y^{6}}{x^{10}}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{8 y^{6}}{x^{6}} \cdot \frac{x^{10}}{y^{6}}$

Step 6

Combine.

$\frac{8 y^{6} x^{10}}{x^{6} y^{6}}$

Step 7

Cancel the common factor of $y^{6}$ .

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Step 7.1

Cancel the common factor.

$\frac{8 y^{6} x^{10}}{x^{6} y^{6}}$

Step 7.2

Rewrite the expression.

$\frac{8 x^{10}}{x^{6}}$

Step 8

Cancel the common factor of $x^{10}$ and $x^{6}$ .

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Step 8.1

Factor $x^{6}$ out of $8 x^{10}$ .

$\frac{x^{6} (8 x^{4})}{x^{6}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Multiply by $1$ .

$\frac{x^{6} (8 x^{4})}{x^{6} \cdot 1}$

Step 8.2.2

Cancel the common factor.

$\frac{x^{6} (8 x^{4})}{x^{6} \cdot 1}$

Step 8.2.3

Rewrite the expression.

$\frac{8 x^{4}}{1}$

Step 8.2.4

Divide $8 x^{4}$ by $1$ .

$8 x^{4}$