Simplify (x^2y^3)^4

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

Step 1

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

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

Step 2

Multiply the exponents in ${(x^{2})}^{4}$ .

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

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

Multiply $2$ by $4$ .

$x^{8} {(y^{3})}^{4}$

Step 3

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

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

$x^{8} y^{3 \cdot 4}$

Multiply $3$ by $4$ .

$x^{8} y^{12}$