Question

which expression is equivalent to (sqrt6{x^{3}y^{4}})?
a (x^{2}y^{4})
b (x^{2}y^{\frac{2}{3}})
c (x^{\frac{1}{2}}y^{\frac{8}{2}})
d (x^{\frac{1}{2}}y^{\frac{2}{3}})

Explanation:

Step1: Convert root to rational exponent

$\sqrt[6]{x^3y^4}=(x^3y^4)^{\frac{1}{6}}$

Step2: Distribute exponent to each term

$(x^3)^{\frac{1}{6}}(y^4)^{\frac{1}{6}}$

Step3: Simplify exponents via multiplication

$x^{\frac{3}{6}}y^{\frac{4}{6}} = x^{\frac{1}{2}}y^{\frac{2}{3}}$

Answer:

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