Algebra Examples

${(\frac{a^{2} b^{- 4}}{b^{2}})}^{5}$

Step 1

Move $b^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{a^{2}}{b^{2} b^{4}})}^{5}$

Step 2

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

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Step 2.1

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

${(\frac{a^{2}}{b^{2 + 4}})}^{5}$

Step 2.2

Add $2$ and $4$ .

${(\frac{a^{2}}{b^{6}})}^{5}$

Step 3

Apply the product rule to $\frac{a^{2}}{b^{6}}$ .

$\frac{{(a^{2})}^{5}}{{(b^{6})}^{5}}$

Step 4

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

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Step 4.1

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

$\frac{a^{2 \cdot 5}}{{(b^{6})}^{5}}$

Step 4.2

Multiply $2$ by $5$ .

$\frac{a^{10}}{{(b^{6})}^{5}}$

Step 5

Multiply the exponents in ${(b^{6})}^{5}$ .

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Step 5.1

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

$\frac{a^{10}}{b^{6 \cdot 5}}$

Step 5.2

Multiply $6$ by $5$ .

$\frac{a^{10}}{b^{30}}$