Simplify ((x^(1/2)y)^(2/3))^3

${({(x^{\frac{1}{2}} y)}^{\frac{2}{3}})}^{3}$

Step 1

Multiply the exponents in ${({(x^{\frac{1}{2}} y)}^{\frac{2}{3}})}^{3}$ .

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

${(x^{\frac{1}{2}} y)}^{\frac{2}{3} \cdot 3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x^{\frac{1}{2}} y)}^{\frac{2}{3} \cdot 3}$

Rewrite the expression.

${(x^{\frac{1}{2}} y)}^{2}$

Step 2

Apply the product rule to $x^{\frac{1}{2}} y$ .

${(x^{\frac{1}{2}})}^{2} y^{2}$

Step 3

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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

$x^{\frac{1}{2} \cdot 2} y^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} y^{2}$

Rewrite the expression.

$x^{1} y^{2}$

Step 4

Simplify.

$x y^{2}$