Simplify ((x^5)/-2)^-3

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Multiply $5$ by $3$ .

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