# Write each radical expression using exponents and each exponential expression using radicals. frac{Radical expression Exponential expression}{sqrt[5]{5^{3}}}

Question
Write each radical expression using exponents and each exponential expression using radicals.
$$\frac{Radical\ expression\ Exponential\ expression}{\sqrt[5]{5^{3}}}$$

2020-10-22
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}}.$$

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