The expression equivalent to [tex]\sqrt[6]({g}^{5})[/tex] is [tex]g^{\frac{5}{6} }[/tex].
What is an exponent?
The number of times a number has been multiplied by itself is referred to as an exponent. It could be an integer, a fraction, a negative integer, or a decimal. Powers or indices are other names for exponents. For instance, 6⁵ indicates that we are multiplying 6 by five. It is 6 × 6 × 6 × 6 × 6 in its expanded form.
How to solve this problem?
The expression is [tex]\sqrt[6]({g}^{5})[/tex].
[tex]\sqrt[6]{g}[/tex] can be written as [tex]g^{\frac{1}{6} }[/tex].
Then the given expression can be written as [tex]g^{\frac{5}{6} }[/tex].
Therefore, the expression equivalent to [tex]\sqrt[6]({g}^{5})[/tex], g > 0 is [tex]g^{\frac{5}{6} }[/tex]. So, option D is correct.
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