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.
\(\frac{Radical\ expression\ Exponential\ expression}{\sqrt[5]{5^{3}}}\)

Answers (1)

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
\(5^{\frac{3}{5}}.\)
0

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