Simplify (3xy^2)^(1/2)

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

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

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

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

Apply the product rule to $3 x$ .

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Reorder factors in $3^{\frac{1}{2}} x^{\frac{1}{2}} y$ .

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