Pre-Algebra Examples

${(a^{- 4} b^{2})}^{- 3}$

Step 1

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

${(\frac{1}{a^{4}} b^{2})}^{- 3}$

Step 2

Combine $\frac{1}{a^{4}}$ and $b^{2}$ .

${(\frac{b^{2}}{a^{4}})}^{- 3}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{a^{4}}{b^{2}})}^{3}$

Step 4

Apply the product rule to $\frac{a^{4}}{b^{2}}$ .

$\frac{{(a^{4})}^{3}}{{(b^{2})}^{3}}$

Step 5

Multiply the exponents in ${(a^{4})}^{3}$ .

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Step 5.1

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

$\frac{a^{4 \cdot 3}}{{(b^{2})}^{3}}$

Step 5.2

Multiply $4$ by $3$ .

$\frac{a^{12}}{{(b^{2})}^{3}}$

Step 6

Multiply the exponents in ${(b^{2})}^{3}$ .

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Step 6.1

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

$\frac{a^{12}}{b^{2 \cdot 3}}$

Step 6.2

Multiply $2$ by $3$ .

$\frac{a^{12}}{b^{6}}$