Accuplacer Advanced Algebra and Functions Practice Exam

To express \( a^{\frac{x}{y}} \) using the fractional exponent rule, we recognize that the expression represents the \( y \)-th root of \( a^x \). According to the rules of exponents, a fractional exponent can be interpreted as:

\[

a^{\frac{x}{y}} = \sqrt[y]{a^x}

\]

This indicates that you take the \( y \)-th root of the quantity \( a^x \). The \( y \)-th root operation can also be expressed using radical notation.

When analyzing the correct answer, it correctly identifies that expressing \( a^{\frac{x}{y}} \) requires taking the \( y \)-th root of \( a^x \). Thus, it represents \( y\sqrt{a^x} \) as the right interpretation, meaning you first find \( a^x \) and then take the \( y \)-th root.

In contrast, the other choices do not accurately reflect the meaning of the fractional exponent as defined by exponent rules. For example, \( \sqrt{a^x} \) only captures the case when \( y = 2 \), while \( (a^x)^y \)