Question

which exponential expression is equivalent to $sqrt6{k^5}$?
choose 1 answer:
a $k^{\frac{6}{5}}$
b $\frac{k^6}{k^5}$
c $\frac{k^5}{k^6}$
d $k^{\frac{5}{6}}$

Explanation:

Step1: Recall the root to exponent rule

The rule for converting a radical to an exponential form is $\sqrt[n]{a^m} = a^{\frac{m}{n}}$. Here, $n = 6$ (the index of the sixth root) and $m = 5$ (the exponent of the base inside the root), and the base $a = k$.

Step2: Apply the rule to $\sqrt[6]{k^5}$

Using the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, substitute $n = 6$, $m = 5$, and $a = k$. So we get $k^{\frac{5}{6}}$.

Answer:

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