Simplify (4x^2y^3)^3

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

Step 1

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

Apply the product rule to $4 x^{2} y^{3}$ .

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

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

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

Step 2

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

$64 {(x^{2})}^{3} {(y^{3})}^{3}$

Step 3

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

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

$64 x^{2 \cdot 3} {(y^{3})}^{3}$

Multiply $2$ by $3$ .

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

Step 4

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

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

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

Multiply $3$ by $3$ .

$64 x^{6} y^{9}$