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

Write each radical expression using exponents and each exponential expression using radicals.
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Sally Cresswell

Given:
The radical expression $\sqrt[5]{{5}^{3}}$
Calculation:
Note that m, n in I and n is positive.
Use the definition, ${a}^{\frac{m}{n}}=\left(\sqrt[a]{a}{\right)}^{m}=\sqrt[n]{{a}^{m}}.$
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
${5}^{\frac{3}{5}}.$