Evaluate ((2c^4)/5)^-3

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

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 2

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

Apply the product rule to $\frac{5}{2 c^{4}}$ .

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

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

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

Step 3

Raise $5$ to the power of $3$ .

$\frac{125}{2^{3} {(c^{4})}^{3}}$

Step 4

Simplify the denominator.

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

$\frac{125}{8 {(c^{4})}^{3}}$

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

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

$\frac{125}{8 c^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{125}{8 c^{12}}$