Pre-Algebra Examples

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

Step 1

Move the negative in front of the fraction.

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

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 $- \frac{a^{4}}{4 b^{3}}$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 3

Simplify the expression.

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Multiply $4$ by $3$ .

$- \frac{a^{12}}{4^{3} {(b^{3})}^{3}}$

Step 4

Simplify the denominator.

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Step 4.1

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

$- \frac{a^{12}}{64 {(b^{3})}^{3}}$

Step 4.2

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

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Step 4.2.1

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

$- \frac{a^{12}}{64 b^{3 \cdot 3}}$

Step 4.2.2

Multiply $3$ by $3$ .

$- \frac{a^{12}}{64 b^{9}}$