Question

what is $sqrt4{7^3}$ in exponential form? $7^{\frac{3}{4}}$ $7^{-\frac{1}{4}}$ $7^{\frac{1}{4}}$

Explanation:

Step1: Recall the root to exponent rule

The rule for converting a root to an exponential form is $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. Here, $n = 4$ (the index of the fourth root) and $m = 3$ (the exponent of the base 7 inside the root).

Step2: Apply the rule

Substitute $n = 4$ and $m = 3$ into the formula $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. So we get $7^{\frac{3}{4}}$.

Answer:

$7^{\frac{3}{4}}$ (corresponding to the first option with the value $7^{\frac{3}{4}}$)