Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

$\frac{1}{{(\frac{y}{4})}^{- 2} {(\frac{x}{2})}^{2}}$

Step 1.2

Move ${(\frac{y}{4})}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $\frac{y}{4}$ .

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

Step 2.2

Raise $4$ to the power of $2$ .

$\frac{\frac{y^{2}}{16}}{{(\frac{x}{2})}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{\frac{y^{2}}{16}}{\frac{x^{2}}{2^{2}}}$

Step 3.2

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

$\frac{\frac{y^{2}}{16}}{\frac{x^{2}}{4}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{y^{2}}{16} \cdot \frac{4}{x^{2}}$

Step 5

Combine.

$\frac{y^{2} \cdot 4}{16 x^{2}}$

Step 6

Cancel the common factor of $4$ and $16$ .

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Step 6.1

Factor $4$ out of $y^{2} \cdot 4$ .

$\frac{4 \cdot y^{2}}{16 x^{2}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $16 x^{2}$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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