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

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

Step 1

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

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

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

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

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

Step 2

Raise $2$ to the power of $3$ .

$8 {(x^{3})}^{3} {(y^{2})}^{3}$

Step 3

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

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

$8 x^{3 \cdot 3} {(y^{2})}^{3}$

Multiply $3$ by $3$ .

$8 x^{9} {(y^{2})}^{3}$

Step 4

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

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

$8 x^{9} y^{2 \cdot 3}$

Multiply $2$ by $3$ .

$8 x^{9} y^{6}$