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

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

Simplify the denominator.

Apply the product rule to $- 2 n^{4}$ .

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

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

$\frac{n^{5}}{- 8 {(n^{4})}^{3}}$

Multiply the exponents in ${(n^{4})}^{3}$ .

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

$\frac{n^{5}}{- 8 n^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{n^{5}}{- 8 n^{12}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $n^{5}$ and $n^{12}$ .

Multiply by $1$ .

$\frac{n^{5} \cdot 1}{- 8 n^{12}}$

Cancel the common factors.

Factor $n^{5}$ out of $- 8 n^{12}$ .

$\frac{n^{5} \cdot 1}{n^{5} (- 8 n^{7})}$

Cancel the common factor.

$\frac{n^{5} \cdot 1}{n^{5} (- 8 n^{7})}$

Rewrite the expression.

$\frac{1}{- 8 n^{7}}$

Move the negative in front of the fraction.

$- \frac{1}{8 n^{7}}$