Algebra Examples

$(\frac{b^{- 2}}{a^{- 2}}) {(\frac{b}{a})}^{2}$

Step 1

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

$\frac{\frac{1}{b^{2}}}{a^{- 2}} {(\frac{b}{a})}^{2}$

Step 2

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

$\frac{\frac{1}{b^{2}}}{\frac{1}{a^{2}}} {(\frac{b}{a})}^{2}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{b^{2}} a^{2} {(\frac{b}{a})}^{2}$

Step 4

Combine $\frac{1}{b^{2}}$ and $a^{2}$ .

$\frac{a^{2}}{b^{2}} {(\frac{b}{a})}^{2}$

Step 5

Apply the product rule to $\frac{b}{a}$ .

$\frac{a^{2}}{b^{2}} \cdot \frac{b^{2}}{a^{2}}$

Step 6

Combine.

$\frac{a^{2} b^{2}}{b^{2} a^{2}}$

Step 7

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

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Step 7.1

Cancel the common factor.

$\frac{a^{2} b^{2}}{b^{2} a^{2}}$

Step 7.2

Rewrite the expression.

$\frac{b^{2}}{b^{2}}$

Step 8

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

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Step 8.1

Cancel the common factor.

$\frac{b^{2}}{b^{2}}$

Step 8.2

Rewrite the expression.

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