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

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

• A. √a^x
• B. y√a^x
• C. (a^x)^y
• D. √y(a^x)

Answer: (B)

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 \( (a^x)^y \)

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 )