Given:

The radical expression \(\sqrt[5]{5^{3}}\)

Calculation:

In the given radical expression, \(m = 3,\ n = 5\ and\ a = 5.\)

Note that m, n in I and n is positive.

Use the definition, \(a^{\frac{m}{n}}=(\sqrt[a]{a})^{m}=\sqrt[n]{a^{m}}.\)

We have \(\sqrt[5]{5^{3}}=5^{\frac{3}{5}}\)

Final Statement:

Thus, the radical expression \(\sqrt[5]{5^{3}}\\) is equivalent to the exponential expressio

\(5^{\frac{3}{5}}.\)

The radical expression \(\sqrt[5]{5^{3}}\)

Calculation:

In the given radical expression, \(m = 3,\ n = 5\ and\ a = 5.\)

Note that m, n in I and n is positive.

Use the definition, \(a^{\frac{m}{n}}=(\sqrt[a]{a})^{m}=\sqrt[n]{a^{m}}.\)

We have \(\sqrt[5]{5^{3}}=5^{\frac{3}{5}}\)

Final Statement:

Thus, the radical expression \(\sqrt[5]{5^{3}}\\) is equivalent to the exponential expressio

\(5^{\frac{3}{5}}.\)