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

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

Step 1

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

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

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

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

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

Step 2

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Simplify.

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

Step 4

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Simplify.

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

Step 6

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

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