Simplify ((4c^-5)/(8d^0))^3

${(\frac{4 c^{- 5}}{8 d^{0}})}^{3}$

Reduce the expression by cancelling the common factors.

Move $c^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{4}{8 d^{0} c^{5}})}^{3}$

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4$ .

${(\frac{4 (1)}{8 d^{0} c^{5}})}^{3}$

Cancel the common factors.

Factor $4$ out of $8 d^{0} c^{5}$ .

${(\frac{4 (1)}{4 (2 d^{0} c^{5})})}^{3}$

Cancel the common factor.

${(\frac{4 \cdot 1}{4 (2 d^{0} c^{5})})}^{3}$

Rewrite the expression.

${(\frac{1}{2 d^{0} c^{5}})}^{3}$

Simplify the denominator.

Anything raised to $0$ is $1$ .

${(\frac{1}{2 \cdot 1 c^{5}})}^{3}$

Multiply $2$ by $1$ .

${(\frac{1}{2 c^{5}})}^{3}$

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

Apply the product rule to $\frac{1}{2 c^{5}}$ .

$\frac{1^{3}}{{(2 c^{5})}^{3}}$

Apply the product rule to $2 c^{5}$ .

$\frac{1^{3}}{2^{3} {(c^{5})}^{3}}$

One to any power is one.

$\frac{1}{2^{3} {(c^{5})}^{3}}$

Simplify the denominator.

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

$\frac{1}{8 {(c^{5})}^{3}}$

Multiply the exponents in ${(c^{5})}^{3}$ .

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

$\frac{1}{8 c^{5 \cdot 3}}$

Multiply $5$ by $3$ .

$\frac{1}{8 c^{15}}$