To determine which property of exponents to use first in the expression [tex]\(\left(x y^2\right)^{\frac{1}{3}}\)[/tex], let's analyze the expression step by step.
Given expression:
[tex]\[
\left(x y^2\right)^{\frac{1}{3}}
\][/tex]
We need to distribute the exponent [tex]\(\frac{1}{3}\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(y^2\)[/tex] inside the parentheses. This is done using the property of exponents for a product. Specifically, we use:
[tex]\[
(a b)^n = a^n b^n
\][/tex]
Applying this property to [tex]\(\left(x y^2\right)^{\frac{1}{3}}\)[/tex], we get:
[tex]\[
(x y^2)^{\frac{1}{3}} = x^{\frac{1}{3}} (y^2)^{\frac{1}{3}}
\][/tex]
Therefore, the correct property of exponents that must be used first is:
B. [tex]\((a b)^n = a^n b^n\)[/tex]
Hence, the correct answer is option B.
