Simplify (5u^4)/((-3u^4)^2)

$\frac{5 u^{4}}{{(- 3 u^{4})}^{2}}$

Simplify the denominator.

Apply the product rule to $- 3 u^{4}$ .

$\frac{5 u^{4}}{{(- 3)}^{2} {(u^{4})}^{2}}$

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

$\frac{5 u^{4}}{9 {(u^{4})}^{2}}$

Multiply the exponents in ${(u^{4})}^{2}$ .

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

$\frac{5 u^{4}}{9 u^{4 \cdot 2}}$

Multiply $4$ by $2$ .

$\frac{5 u^{4}}{9 u^{8}}$

Cancel the common factor of $u^{4}$ and $u^{8}$ .

Factor $u^{4}$ out of $5 u^{4}$ .

$\frac{u^{4} \cdot 5}{9 u^{8}}$

Cancel the common factors.

Factor $u^{4}$ out of $9 u^{8}$ .

$\frac{u^{4} \cdot 5}{u^{4} (9 u^{4})}$

Cancel the common factor.

$\frac{u^{4} \cdot 5}{u^{4} (9 u^{4})}$

Rewrite the expression.

$\frac{5}{9 u^{4}}$