Question

which of the following is equivalent to $sqrt5{13^3}$?
$13^{\frac{3}{5}}$ $13^2$ $13^{15}$ $13^{\frac{5}{3}}$

Explanation:

Step1: Recall the radical exponent rule

The rule for converting a radical to an exponent is $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. Here, we have $\sqrt[5]{13^3}$, so $n = 5$ and $m = 3$.

Step2: Apply the rule

Using the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, substitute $a = 13$, $m = 3$, and $n = 5$. So $\sqrt[5]{13^3}=13^{\frac{3}{5}}$.

Answer:

$13^{\frac{3}{5}}$ (the top - middle option among the given choices)