Answer :
Certainly! Let's break down the expression \(\sqrt[11]{a^6}\) step-by-step into its exponential form.
1. Understanding Roots and Exponents:
- The nth root of a number can be expressed as an exponent. Specifically, the nth root of \(a^m\) can be written as \(a^{m/n}\).
2. Applying to the Given Expression:
- Here, we have the 11th root of \(a^6\). We can express this in exponential form by noting that the nth root corresponds to the exponent \(1/n\).
3. Formulating the Exponent:
- The exponent \(m/n\) for this expression will have \(m = 6\) and \(n = 11\).
- Therefore, \(\sqrt[11]{a^6}\) can be written as \(a^{6/11}\).
4. Result:
- Thus, the expression \(\sqrt[11]{a^6}\) in exponential form is:
[tex]\[ a^{6/11} \][/tex]
So the final answer is [tex]\(\boxed{a^{6/11}}\)[/tex].
1. Understanding Roots and Exponents:
- The nth root of a number can be expressed as an exponent. Specifically, the nth root of \(a^m\) can be written as \(a^{m/n}\).
2. Applying to the Given Expression:
- Here, we have the 11th root of \(a^6\). We can express this in exponential form by noting that the nth root corresponds to the exponent \(1/n\).
3. Formulating the Exponent:
- The exponent \(m/n\) for this expression will have \(m = 6\) and \(n = 11\).
- Therefore, \(\sqrt[11]{a^6}\) can be written as \(a^{6/11}\).
4. Result:
- Thus, the expression \(\sqrt[11]{a^6}\) in exponential form is:
[tex]\[ a^{6/11} \][/tex]
So the final answer is [tex]\(\boxed{a^{6/11}}\)[/tex].
