Simplify (3x^2*2x^2)^2

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

Rewrite using the commutative property of multiplication.

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

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(3 \cdot 2 x^{2 + 2})}^{2}$

Add $2$ and $2$ .

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

Multiply $3$ by $2$ .

${(6 x^{4})}^{2}$

Apply the product rule to $6 x^{4}$ .

$6^{2} {(x^{4})}^{2}$

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

$36 {(x^{4})}^{2}$

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

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

$36 x^{4 \cdot 2}$

Multiply $4$ by $2$ .

$36 x^{8}$