Evaluate (2xy^3)^4

${(2 x y^{3})}^{4}$

Step 1

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

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

${(2 x)}^{4} {(y^{3})}^{4}$

Apply the product rule to $2 x$ .

$2^{4} x^{4} {(y^{3})}^{4}$

Step 2

Raise $2$ to the power of $4$ .

$16 x^{4} {(y^{3})}^{4}$

Step 3

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

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

$16 x^{4} y^{3 \cdot 4}$

Multiply $3$ by $4$ .

$16 x^{4} y^{12}$