Simplify 4(150x^2y)^(1/2)

$4 {(150 x^{2} y)}^{\frac{1}{2}}$

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

Apply the product rule to $150 x^{2} y$ .

$4 ({(150 x^{2})}^{\frac{1}{2}} y^{\frac{1}{2}})$

Apply the product rule to $150 x^{2}$ .

$4 (150^{\frac{1}{2}} {(x^{2})}^{\frac{1}{2}} y^{\frac{1}{2}})$

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

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

$4 (150^{\frac{1}{2}} x^{2 (\frac{1}{2})} y^{\frac{1}{2}})$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 (150^{\frac{1}{2}} x^{2 (\frac{1}{2})} y^{\frac{1}{2}})$

Rewrite the expression.

$4 (150^{\frac{1}{2}} x^{1} y^{\frac{1}{2}})$

Simplify.

$4 (150^{\frac{1}{2}} x y^{\frac{1}{2}})$

Reorder factors in $4 \cdot 150^{\frac{1}{2}} x y^{\frac{1}{2}}$ .

$4 x \cdot 150^{\frac{1}{2}} y^{\frac{1}{2}}$