Algebra Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

Apply the product rule to $x y$ .

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

Step 2.3

Multiply $y^{3}$ by $y^{3}$ by adding the exponents.

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Step 2.3.1

Move $y^{3}$ .

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

Step 2.3.2

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

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

Step 2.3.3

Add $3$ and $3$ .

$\frac{1}{{(x^{- 5})}^{3} y^{6} x^{3}}$

Step 2.4

Multiply the exponents in ${(x^{- 5})}^{3}$ .

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Step 2.4.1

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

$\frac{1}{x^{- 5 \cdot 3} y^{6} x^{3}}$

Step 2.4.2

Multiply $- 5$ by $3$ .

$\frac{1}{x^{- 15} y^{6} x^{3}}$

Step 2.5

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

$\frac{1}{\frac{1}{x^{15}} y^{6} x^{3}}$

Step 2.6

Combine exponents.

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Step 2.6.1

Combine $\frac{1}{x^{15}}$ and $y^{6}$ .

$\frac{1}{\frac{y^{6}}{x^{15}} x^{3}}$

Step 2.6.2

Combine $\frac{y^{6}}{x^{15}}$ and $x^{3}$ .

$\frac{1}{\frac{y^{6} x^{3}}{x^{15}}}$

Step 2.7

Reduce the expression $\frac{y^{6} x^{3}}{x^{15}}$ by cancelling the common factors.

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Step 2.7.1

Factor $x^{3}$ out of $y^{6} x^{3}$ .

$\frac{1}{\frac{x^{3} y^{6}}{x^{15}}}$

Step 2.7.2

Factor $x^{3}$ out of $x^{15}$ .

$\frac{1}{\frac{x^{3} y^{6}}{x^{3} x^{12}}}$

Step 2.7.3

Cancel the common factor.

$\frac{1}{\frac{x^{3} y^{6}}{x^{3} x^{12}}}$

Step 2.7.4

Rewrite the expression.

$\frac{1}{\frac{y^{6}}{x^{12}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{x^{12}}{y^{6}}$

Step 4

Multiply $\frac{x^{12}}{y^{6}}$ by $1$ .

$\frac{x^{12}}{y^{6}}$