Simplify (-2c^-1d^3)^3

${(- 2 c^{- 1} d^{3})}^{3}$

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

${(- 2 \frac{1}{c} d^{3})}^{3}$

Combine $- 2$ and $\frac{1}{c}$ .

${(\frac{- 2}{c} d^{3})}^{3}$

Move the negative in front of the fraction.

${(- \frac{2}{c} d^{3})}^{3}$

Combine $d^{3}$ and $\frac{2}{c}$ .

${(- \frac{d^{3} \cdot 2}{c})}^{3}$

Move $2$ to the left of $d^{3}$ .

${(- \frac{2 \cdot d^{3}}{c})}^{3}$

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

Apply the product rule to $- \frac{2 d^{3}}{c}$ .

${(- 1)}^{3} {(\frac{2 d^{3}}{c})}^{3}$

Apply the product rule to $\frac{2 d^{3}}{c}$ .

${(- 1)}^{3} \frac{{(2 d^{3})}^{3}}{c^{3}}$

Apply the product rule to $2 d^{3}$ .

${(- 1)}^{3} \frac{2^{3} {(d^{3})}^{3}}{c^{3}}$

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

$- \frac{2^{3} {(d^{3})}^{3}}{c^{3}}$

Simplify the numerator.

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

$- \frac{8 {(d^{3})}^{3}}{c^{3}}$

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

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

$- \frac{8 d^{3 \cdot 3}}{c^{3}}$

Multiply $3$ by $3$ .

$- \frac{8 d^{9}}{c^{3}}$