Evaluate (2x^3y)^6

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

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

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

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

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

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

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

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

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

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

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

Multiply $3$ by $6$ .

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