given that the meaning of a rational exponent can be connected to the meaning of the root how can you rewrite 3/5 using a rational exponent?

A rational exponent of the form \( \frac{m}{n} \) can be expressed as \( a^{\frac{m}{n}} = \sqrt[n]{a^m} \), where \( a \) is any real number, \( m \) is an integer, and \( n \) is a positive integer.

To rewrite \( \frac{3}{5} \) using a rational exponent, you can interpret \( 3 \) as the power and \( 5 \) as the root. Therefore, \( \frac{3}{5} \) can be expressed as:

\[
a^{\frac{3}{5}} = \sqrt[5]{a^3}
\]

So, \( 3/5 \) rewritten using a rational exponent indicates taking the fifth root of \( a \) raised to the third power.

For example, if \( a = x \), then:
\[
x^{\frac{3}{5}} = \sqrt[5]{x^3}
\]