Simplify (a^2b^3)^2

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

Step 1

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

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

Step 2

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

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

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

Multiply $2$ by $2$ .

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

Step 3

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

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

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

Multiply $3$ by $2$ .

$a^{4} b^{6}$