Algebra Examples

${(- \frac{q^{4}}{5})}^{- 3}$

Step 1

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

${(- \frac{5}{q^{4}})}^{3}$

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 $- \frac{5}{q^{4}}$ .

${(- 1)}^{3} {(\frac{5}{q^{4}})}^{3}$

Step 2.2

Apply the product rule to $\frac{5}{q^{4}}$ .

${(- 1)}^{3} \frac{5^{3}}{{(q^{4})}^{3}}$

Step 3

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

$- \frac{5^{3}}{{(q^{4})}^{3}}$

Step 4

Raise $5$ to the power of $3$ .

$- \frac{125}{{(q^{4})}^{3}}$

Step 5

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

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Step 5.1

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

$- \frac{125}{q^{4 \cdot 3}}$

Step 5.2

Multiply $4$ by $3$ .

$- \frac{125}{q^{12}}$