Algebra Examples

${(\frac{x^{5}}{- 2})}^{- 3}$

Step 1

Move the negative in front of the fraction.

${(- \frac{x^{5}}{2})}^{- 3}$

Step 2

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

${(- \frac{2}{x^{5}})}^{3}$

Step 3

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

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Step 3.1

Apply the product rule to $- \frac{2}{x^{5}}$ .

${(- 1)}^{3} {(\frac{2}{x^{5}})}^{3}$

Step 3.2

Apply the product rule to $\frac{2}{x^{5}}$ .

${(- 1)}^{3} \frac{2^{3}}{{(x^{5})}^{3}}$

Step 4

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

$- \frac{2^{3}}{{(x^{5})}^{3}}$

Step 5

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

$- \frac{8}{{(x^{5})}^{3}}$

Step 6

Multiply the exponents in ${(x^{5})}^{3}$ .

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Step 6.1

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

$- \frac{8}{x^{5 \cdot 3}}$

Step 6.2

Multiply $5$ by $3$ .

$- \frac{8}{x^{15}}$