Simplify (-4z^3)^-3

${(- 4 z^{3})}^{- 3}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(- 4 z^{3})}^{3}}$

Step 2

Simplify the denominator.

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

$\frac{1}{{(- 4)}^{3} {(z^{3})}^{3}}$

Raise $- 4$ to the power of $3$ .

$\frac{1}{- 64 {(z^{3})}^{3}}$

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

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

$\frac{1}{- 64 z^{3 \cdot 3}}$

Multiply $3$ by $3$ .

$\frac{1}{- 64 z^{9}}$

Step 3

Move the negative in front of the fraction.

$- \frac{1}{64 z^{9}}$