To simplify the expression [tex]\(\left(x y^2\right)^{\frac{1}{3}}\)[/tex], you need to apply the properties of exponents in the correct order to break it down step-by-step.
In this specific problem, you need to raise both the [tex]\(x\)[/tex] and [tex]\(y^2\)[/tex] inside the parentheses to the power of [tex]\(\frac{1}{3}\)[/tex] because this encompasses the entire product within the parentheses.
Therefore, the property of exponents you should use first is:
D. [tex]\((a b)^n = a^n b^n\)[/tex]
This property allows you to distribute the exponent [tex]\(\frac{1}{3}\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(y^2\)[/tex] individually:
[tex]$
\left(x y^2\right)^{\frac{1}{3}} = x^{\frac{1}{3}} (y^2)^{\frac{1}{3}}
$[/tex]
