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

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

Step 1

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

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

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

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

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

Step 2

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

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

Step 3

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

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

$9 x^{2 \cdot 2} {(y^{3})}^{2}$

Multiply $2$ by $2$ .

$9 x^{4} {(y^{3})}^{2}$

Step 4

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

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

$9 x^{4} y^{3 \cdot 2}$

Multiply $3$ by $2$ .

$9 x^{4} y^{6}$