Pre-Algebra Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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Step 2.1

Apply the product rule to $- \frac{4 a}{b^{3}}$ .

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

Step 2.2

Apply the product rule to $\frac{4 a}{b^{3}}$ .

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

Step 2.3

Apply the product rule to $4 a$ .

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

Step 3

Raise $- 1$ to the power of $3$ .

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

Step 4

Raise $4$ to the power of $3$ .

$- \frac{64 a^{3}}{{(b^{3})}^{3}}$

Step 5

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

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Step 5.1

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

$- \frac{64 a^{3}}{b^{3 \cdot 3}}$

Step 5.2

Multiply $3$ by $3$ .

$- \frac{64 a^{3}}{b^{9}}$