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

. What is the simplified exponent?(1 point)

1 answer

To solve the expression \( \frac{9^{3/5}}{9^{1/5}} \) using the Quotient Property of exponents, we can use the property that states:

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

In this case, we have:

  • \( a = 9 \)
  • \( m = \frac{3}{5} \)
  • \( n = \frac{1}{5} \)

Now, applying the Quotient Property:

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

Now, we subtract the exponents:

\[ 3/5 - 1/5 = \frac{3-1}{5} = \frac{2}{5} \]

Thus, the expression simplifies to:

\[ 9^{2/5} \]

The simplified exponent is:

\[ \frac{2}{5} \]