Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

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Step 2.5.1

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

$\frac{y w^{3}}{\frac{x^{2 \cdot 2}}{{(y^{2})}^{2}} w^{2} x^{2}}$

Step 2.5.2

Multiply $2$ by $2$ .

$\frac{y w^{3}}{\frac{x^{4}}{{(y^{2})}^{2}} w^{2} x^{2}}$

Step 2.6

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

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Step 2.6.1

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

$\frac{y w^{3}}{\frac{x^{4}}{y^{2 \cdot 2}} w^{2} x^{2}}$

Step 2.6.2

Multiply $2$ by $2$ .

$\frac{y w^{3}}{\frac{x^{4}}{y^{4}} w^{2} x^{2}}$

Step 2.7

Combine exponents.

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Step 2.7.1

Combine $\frac{x^{4}}{y^{4}}$ and $w^{2}$ .

$\frac{y w^{3}}{\frac{x^{4} w^{2}}{y^{4}} x^{2}}$

Step 2.7.2

Combine $\frac{x^{4} w^{2}}{y^{4}}$ and $x^{2}$ .

$\frac{y w^{3}}{\frac{x^{4} w^{2} x^{2}}{y^{4}}}$

Step 2.7.3

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

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Step 2.7.3.1

Move $x^{2}$ .

$\frac{y w^{3}}{\frac{x^{2} x^{4} w^{2}}{y^{4}}}$

Step 2.7.3.2

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

$\frac{y w^{3}}{\frac{x^{2 + 4} w^{2}}{y^{4}}}$

Step 2.7.3.3

Add $2$ and $4$ .

$\frac{y w^{3}}{\frac{x^{6} w^{2}}{y^{4}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$y w^{3} \frac{y^{4}}{x^{6} w^{2}}$

Step 4

Cancel the common factor of $w^{2}$ .

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Step 4.1

Factor $w^{2}$ out of $y w^{3}$ .

$w^{2} (y w) \frac{y^{4}}{x^{6} w^{2}}$

Step 4.2

Factor $w^{2}$ out of $x^{6} w^{2}$ .

$w^{2} (y w) \frac{y^{4}}{w^{2} x^{6}}$

Step 4.3

Cancel the common factor.

$w^{2} (y w) \frac{y^{4}}{w^{2} x^{6}}$

Step 4.4

Rewrite the expression.

$y w \frac{y^{4}}{x^{6}}$

Step 5

Combine $y$ and $\frac{y^{4}}{x^{6}}$ .

$w \frac{y \cdot y^{4}}{x^{6}}$

Step 6

Multiply $y$ by $y^{4}$ by adding the exponents.

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Step 6.1

Multiply $y$ by $y^{4}$ .

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Step 6.1.1

Raise $y$ to the power of $1$ .

$w \frac{y^{1} y^{4}}{x^{6}}$

Step 6.1.2

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

$w \frac{y^{1 + 4}}{x^{6}}$

Step 6.2

Add $1$ and $4$ .

$w \frac{y^{5}}{x^{6}}$

Step 7

Combine $w$ and $\frac{y^{5}}{x^{6}}$ .

$\frac{w y^{5}}{x^{6}}$