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

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

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

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

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

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

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

Apply the product rule to $3 u^{3}$ .

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

Simplify the numerator.

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

$- \frac{9 {(u^{3})}^{2}}{5^{2}}$

Multiply the exponents in ${(u^{3})}^{2}$ .

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

$- \frac{9 u^{3 \cdot 2}}{5^{2}}$

Multiply $3$ by $2$ .

$- \frac{9 u^{6}}{5^{2}}$

Raise $5$ to the power of $2$ .

$- \frac{9 u^{6}}{25}$