According to the fractional exponent rule, how is a^x/y expressed?

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 )