select the correct answer. which expression is equivalent to $sqrt6{g^{5}}$, if $g > 0$?\na…

select the correct answer. which expression is equivalent to $sqrt6{g^{5}}$, if $g > 0$?\na. $g^{\frac{6}{5}}$\nb. $5g^{6}$\nc. $\frac{5}{6}g$\nd. $g^{\frac{5}{6}}$

select the correct answer. which expression is equivalent to $sqrt6{g^{5}}$, if $g > 0$?\na. $g^{\frac{6}{5}}$\nb. $5g^{6}$\nc. $\frac{5}{6}g$\nd. $g^{\frac{5}{6}}$

Answer

Explanation:

Step1: Recall the radical - exponent rule

The rule for converting a radical $\sqrt[n]{a^m}$ to an exponential form is $a^{\frac{m}{n}}$, where $n$ is the index of the radical and $m$ is the exponent of the base inside the radical.

Step2: Apply the rule to the given expression

For the expression $\sqrt[6]{g^{5}}$, here $n = 6$ and $m = 5$. By the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, we get $g^{\frac{5}{6}}$.

Answer:

D. $g^{\frac{5}{6}}$