Find the Product (a^2b^3)^4

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

Step 1

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

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

Step 2

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

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

$a^{2 \cdot 4} {(b^{3})}^{4}$

Multiply $2$ by $4$ .

$a^{8} {(b^{3})}^{4}$

Step 3

Multiply the exponents in ${(b^{3})}^{4}$ .

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

$a^{8} b^{3 \cdot 4}$

Multiply $3$ by $4$ .

$a^{8} b^{12}$