Question

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

Explanation:

Step1: Recall the radical exponent rule

The rule for converting a radical to an exponent is $\sqrt[n]{a^m}=a^{\frac{m}{n}}$.

Step2: Apply the rule to the given expression

For $\sqrt[5]{13^3}$, here $n = 5$ and $m = 3$. So applying the rule, we get $13^{\frac{3}{5}}$.

Answer:

$13^{\frac{3}{5}}$ (the third option among the visible ones, with the expression $13^{\frac{3}{5}}$)