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

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

Step 1

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

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

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

Apply the product rule to $3 x$ .

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

Step 2

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

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

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

Combine $3$ and $\frac{1}{2}$ .

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