Simplify (2/(5m^5))^-4

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

Step 1

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

${(\frac{5 m^{5}}{2})}^{4}$

Step 2

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

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

$\frac{{(5 m^{5})}^{4}}{2^{4}}$

Apply the product rule to $5 m^{5}$ .

$\frac{5^{4} {(m^{5})}^{4}}{2^{4}}$

Step 3

Simplify the numerator.

Raise $5$ to the power of $4$ .

$\frac{625 {(m^{5})}^{4}}{2^{4}}$

Multiply the exponents in ${(m^{5})}^{4}$ .

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

$\frac{625 m^{5 \cdot 4}}{2^{4}}$

Multiply $5$ by $4$ .

$\frac{625 m^{20}}{2^{4}}$

Step 4

Raise $2$ to the power of $4$ .

$\frac{625 m^{20}}{16}$