When I write my expression in rational exponent form, what is the fraction that goes with the base of 10?

Answer is the fraction 3/5
The rule to use here is
[tex]\sqrt[n]{x^m} = x^{m/n}[/tex]
The n is the index of the root, which is the denominator of the fractional exponent. In this case, x = 10, m = 3, n = 5
So,
[tex]\sqrt[5]{10^3} = 10^{3/5}[/tex]