Simplify the Radical Expression (xy^(2/3))^(1/2)

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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