Question

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

Explanation:

Step1: Recall the radical to exponent rule

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

Step2: Apply the rule to the given expression

Substitute the values into the formula: $\sqrt[5]{13^3}=13^{\frac{3}{5}}$.

Answer:

$13^{\frac{3}{5}}$ (the last option: $13^{\frac{3}{5}}$)