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

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

Step 1

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

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

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

Multiply $3$ by $2$ .

$2 a^{3} b^{2} b^{6}$

Step 2

Multiply $b^{2}$ by $b^{6}$ by adding the exponents.

Move $b^{6}$ .

$2 a^{3} (b^{6} b^{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 a^{3} b^{6 + 2}$

Add $6$ and $2$ .

$2 a^{3} b^{8}$