Sure! Let's simplify the given expression using the Quotient Property.
The Quotient Property for exponents states that [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex], where [tex]\(a\)[/tex] is the base and [tex]\(m\)[/tex] and [tex]\(n\)[/tex] are the exponents. In this case, the base [tex]\(a\)[/tex] is 9, the numerator exponent [tex]\(m\)[/tex] is [tex]\(\frac{3}{5}\)[/tex], and the denominator exponent [tex]\(n\)[/tex] is [tex]\(\frac{1}{5}\)[/tex].
Following these steps:
1. Identify the exponents: The exponent in the numerator is [tex]\(\frac{3}{5}\)[/tex] and the exponent in the denominator is [tex]\(\frac{1}{5}\)[/tex].
2. Apply the Quotient Property: Subtract the exponent in the denominator from the exponent in the numerator.
[tex]\[
\frac{9^{\frac{3}{5}}}{9^{\frac{1}{5}}} = 9^{\frac{3}{5} - \frac{1}{5}}
\][/tex]
3. Perform the subtraction inside the exponent:
[tex]\[
\frac{3}{5} - \frac{1}{5} = \frac{3 - 1}{5} = \frac{2}{5}
\][/tex]
So, the simplified exponent is [tex]\(\frac{2}{5}\)[/tex].
The result is:
[tex]\[
9^{\frac{2}{5}}
\][/tex]
Therefore, when simplified, the exponent [tex]\(\frac{2}{5}\)[/tex] is the answer.
