Simplify (3y^(2/3))^3(2y^2)^2

${(3 y^{\frac{2}{3}})}^{3} {(2 y^{2})}^{2}$

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

$3^{3} {(y^{\frac{2}{3}})}^{3} {(2 y^{2})}^{2}$

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

$27 {(y^{\frac{2}{3}})}^{3} {(2 y^{2})}^{2}$

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

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

$27 y^{\frac{2}{3} \cdot 3} {(2 y^{2})}^{2}$

Cancel the common factor of $3$ .

Cancel the common factor.

$27 y^{\frac{2}{3} \cdot 3} {(2 y^{2})}^{2}$

Rewrite the expression.

$27 y^{2} {(2 y^{2})}^{2}$

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

$27 y^{2} (2^{2} {(y^{2})}^{2})$

Rewrite using the commutative property of multiplication.

$27 \cdot 2^{2} y^{2} {(y^{2})}^{2}$

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

$27 \cdot 4 y^{2} {(y^{2})}^{2}$

Multiply $27$ by $4$ .

$108 y^{2} {(y^{2})}^{2}$

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

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

$108 y^{2} y^{2 \cdot 2}$

Multiply $2$ by $2$ .

$108 y^{2} y^{4}$

Multiply $y^{2}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$108 (y^{4} y^{2})$

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

$108 y^{4 + 2}$

Add $4$ and $2$ .

$108 y^{6}$