Question

select the correct answer.
which expression is equivalent to $sqrt6{g^{5}}$, if $g > 0$
a. $g^{\frac{6}{5}}$
b. $5g^{6}$
c. $\frac{5}{6}g$
d. $g^{\frac{5}{6}}$

Explanation:

Step1: Apply root-to-exponent rule

Recall that $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ for $a>0$. Here, $n=6$, $m=5$, $a=g$.
$\sqrt[6]{g^5} = g^{\frac{5}{6}}$

Step2: Match with options

Compare the result to the given choices.

Answer:

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