which of the following is equivalent to $sqrt5{13^{3}}$?\n$13^{2}$\n$13^{15}$\n$13^{\frac{5}{3}}$\n$13^{\frac…
which of the following is equivalent to $sqrt5{13^{3}}$?\n$13^{2}$\n$13^{15}$\n$13^{\frac{5}{3}}$\n$13^{\frac{3}{5}}$
Answer
Explanation:
Step1: Recall the radical - exponent rule
The rule for converting a radical $\sqrt[n]{a^m}$ to an exponent is $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. Here, $a = 13$, $m = 3$, and $n = 5$.
Step2: Apply the rule
For the expression $\sqrt[5]{13^{3}}$, using the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, we get $13^{\frac{3}{5}}$.
Answer:
$13^{\frac{3}{5}}$ (corresponding to the last option)