Precalculus Examples

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

Step 1

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

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

Step 2

Multiply $2 a^{2} \frac{1}{b^{3}}$ .

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Step 2.1

Combine $2$ and $\frac{1}{b^{3}}$ .

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

Step 2.2

Combine $a^{2}$ and $\frac{2}{b^{3}}$ .

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

Step 3

Move $2$ to the left of $a^{2}$ .

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

Step 4

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

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

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $\frac{b^{3}}{2 a^{2}}$ .

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

Step 5.2

Apply the product rule to $2 a^{2}$ .

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Multiply $3$ by $3$ .

$\frac{b^{9}}{2^{3} {(a^{2})}^{3}}$

Step 7

Simplify the denominator.

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Step 7.1

Raise $2$ to the power of $3$ .

$\frac{b^{9}}{8 {(a^{2})}^{3}}$

Step 7.2

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

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Step 7.2.1

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

$\frac{b^{9}}{8 a^{2 \cdot 3}}$

Step 7.2.2

Multiply $2$ by $3$ .

$\frac{b^{9}}{8 a^{6}}$