Simplify ((2xy^3)^2)^3

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

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

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

${(2 x y^{3})}^{2 \cdot 3}$

Multiply $2$ by $3$ .

${(2 x y^{3})}^{6}$

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

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

${(2 x)}^{6} {(y^{3})}^{6}$

Apply the product rule to $2 x$ .

$2^{6} x^{6} {(y^{3})}^{6}$

Raise $2$ to the power of $6$ .

$64 x^{6} {(y^{3})}^{6}$

Multiply the exponents in ${(y^{3})}^{6}$ .

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

$64 x^{6} y^{3 \cdot 6}$

Multiply $3$ by $6$ .

$64 x^{6} y^{18}$