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

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

Rewrite using the commutative property of multiplication.

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

Multiply $3$ by $2$ .

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

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

Apply the product rule to $6 x^{3} y^{3}$ .

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

Apply the product rule to $6 x^{3}$ .

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

Raise $6$ to the power of $3$ .

$216 {(x^{3})}^{3} {(y^{3})}^{3}$

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

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

$216 x^{3 \cdot 3} {(y^{3})}^{3}$

Multiply $3$ by $3$ .

$216 x^{9} {(y^{3})}^{3}$

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

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

$216 x^{9} y^{3 \cdot 3}$

Multiply $3$ by $3$ .

$216 x^{9} y^{9}$