Simplify (2^2a^5b^3)^2

${(2^{2} a^{5} b^{3})}^{2}$

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

${(4 a^{5} b^{3})}^{2}$

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

Apply the product rule to $4 a^{5} b^{3}$ .

${(4 a^{5})}^{2} {(b^{3})}^{2}$

Apply the product rule to $4 a^{5}$ .

$4^{2} {(a^{5})}^{2} {(b^{3})}^{2}$

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

$16 {(a^{5})}^{2} {(b^{3})}^{2}$

Multiply the exponents in ${(a^{5})}^{2}$ .

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

$16 a^{5 \cdot 2} {(b^{3})}^{2}$

Multiply $5$ by $2$ .

$16 a^{10} {(b^{3})}^{2}$

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

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

$16 a^{10} b^{3 \cdot 2}$

Multiply $3$ by $2$ .

$16 a^{10} b^{6}$