Question

rewrite the expression \\(\sqrt4{16^2}\\) using a fractional exponent.\\(\sqrt4{16^2} = 16^{\square}\\) (simplify your answer.)

Explanation:

Step1: Recall the radical to exponent rule

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

Step2: Apply the rule to the given expression

For the expression $\sqrt[4]{16^2}$, here $n = 4$ and $m = 2$. So applying the rule, we get $16^{\frac{2}{4}}$.

Step3: Simplify the fraction

Simplify $\frac{2}{4}$ to $\frac{1}{2}$.

Answer:

$\frac{1}{2}$