To determine the equivalent expression for [tex]\(\sqrt[6]{g^5}\)[/tex], we need to convert the radical expression into an expression with exponents.
The general form for converting a [tex]\(n\)[/tex]th root of [tex]\(x^m\)[/tex] is given by:
[tex]\[
\sqrt[n]{x^m} = x^{\frac{m}{n}}
\][/tex]
Applying this rule to [tex]\(\sqrt[6]{g^5}\)[/tex]:
[tex]\[
\sqrt[6]{g^5} = g^{\frac{5}{6}}
\][/tex]
Now, let's compare this result with the given choices:
A. [tex]\(g^{\frac{5}{5}}\)[/tex] simplifies to [tex]\(g^1\)[/tex], which is just [tex]\(g\)[/tex].
B. [tex]\(5 g^6\)[/tex] is simply [tex]\(5 \times g^6\)[/tex], which is not in the form we need.
C. [tex]\(\frac{5}{6} g\)[/tex] is a linear term, not an exponential form that matches our converted expression.
D. [tex]\(g^{\frac{5}{6}}\)[/tex] directly matches our result from the conversion.
Therefore, the correct expression equivalent to [tex]\(\sqrt[6]{g^5}\)[/tex] is:
[tex]\[
\boxed{D}
\][/tex]
