Simplify (8m^3nq^2)^2

${(8 m^{3} n q^{2})}^{2}$

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

Apply the product rule to $8 m^{3} n q^{2}$ .

${(8 m^{3} n)}^{2} {(q^{2})}^{2}$

Apply the product rule to $8 m^{3} n$ .

${(8 m^{3})}^{2} n^{2} {(q^{2})}^{2}$

Apply the product rule to $8 m^{3}$ .

$8^{2} {(m^{3})}^{2} n^{2} {(q^{2})}^{2}$

Raise $8$ to the power of $2$ .

$64 {(m^{3})}^{2} n^{2} {(q^{2})}^{2}$

Multiply the exponents in ${(m^{3})}^{2}$ .

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

$64 m^{3 \cdot 2} n^{2} {(q^{2})}^{2}$

Multiply $3$ by $2$ .

$64 m^{6} n^{2} {(q^{2})}^{2}$

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

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

$64 m^{6} n^{2} q^{2 \cdot 2}$

Multiply $2$ by $2$ .

$64 m^{6} n^{2} q^{4}$