Simplify ((m^5n)/(pq^2))^4

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

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

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

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

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

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

Apply the product rule to $p q^{2}$ .

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

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

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

$\frac{m^{5 \cdot 4} n^{4}}{p^{4} {(q^{2})}^{4}}$

Multiply $5$ by $4$ .

$\frac{m^{20} n^{4}}{p^{4} {(q^{2})}^{4}}$

Multiply the exponents in ${(q^{2})}^{4}$ .

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

$\frac{m^{20} n^{4}}{p^{4} q^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\frac{m^{20} n^{4}}{p^{4} q^{8}}$