Simplify (4a^2b)^3

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

Step 1

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

Apply the product rule to $4 a^{2} b$ .

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

Apply the product rule to $4 a^{2}$ .

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

Step 2

Raise $4$ to the power of $3$ .

$64 {(a^{2})}^{3} b^{3}$

Step 3

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

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

$64 a^{2 \cdot 3} b^{3}$

Multiply $2$ by $3$ .

$64 a^{6} b^{3}$