Question

Use the Quotient Property to generate an equivalent expression to 9^3/5/9^1/5

Answer 1

The Quotient Property of exponents states that when you divide two exponential expressions with the same base, you can subtract their exponents. This can be expressed mathematically as:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

In your case, you have the expression:

\[
\frac{9^{3/5}}{9^{1/5}}
\]

To apply the Quotient Property, subtract the exponents:

\[
9^{3/5 - 1/5}
\]

Now calculate the exponent:

\[
3/5 - 1/5 = (3 - 1)/5 = 2/5
\]

Thus, the expression simplifies to:

\[
9^{2/5}
\]

So, an equivalent expression to \(\frac{9^{3/5}}{9^{1/5}}\) is:

\[
9^{2/5}
\]