Simplify (4xy^2)^(1/2)

${(4 x y^{2})}^{\frac{1}{2}}$

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

Apply the product rule to $4 x y^{2}$ .

${(4 x)}^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}$

Apply the product rule to $4 x$ .

$4^{\frac{1}{2}} x^{\frac{1}{2}} {(y^{2})}^{\frac{1}{2}}$

Simplify the expression.

Rewrite $4$ as $2^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

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

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