Simplify (-(5a)/3)^-3

${(- \frac{5 a}{3})}^{- 3}$

Step 1

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

${(- \frac{3}{5 a})}^{3}$

Step 2

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

Apply the product rule to $- \frac{3}{5 a}$ .

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

Apply the product rule to $\frac{3}{5 a}$ .

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

Apply the product rule to $5 a$ .

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

Step 3

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

$- \frac{3^{3}}{5^{3} a^{3}}$

Step 4

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

$- \frac{27}{5^{3} a^{3}}$

Step 5

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

$- \frac{27}{125 a^{3}}$