Evaluate (2a^3b)^5

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

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

Apply the product rule to $2 a^{3} b$ .

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

Apply the product rule to $2 a^{3}$ .

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

Raise $2$ to the power of $5$ .

$32 {(a^{3})}^{5} b^{5}$

Multiply the exponents in ${(a^{3})}^{5}$ .

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

$32 a^{3 \cdot 5} b^{5}$

Multiply $3$ by $5$ .

$32 a^{15} b^{5}$