Question

which expression is equivalent to \\(sqrt3{6}\\)?
\\(6^3\\) \\(6^{\frac{1}{3}}\\) \\(6^2\\) \\(6^{\frac{1}{2}}\\)

Explanation:

Step1: Recall root-exponent rule

For any positive real number $a$ and positive integer $n$, $\sqrt[n]{a} = a^{\frac{1}{n}}$.

Step2: Apply rule to given expression

Here, $a=6$ and $n=3$, so $\sqrt[3]{6} = 6^{\frac{1}{3}}$.

Answer:

$6^{\frac{1}{3}}$