Question

which expression is equivalent to \\(\sqrt3{6^2}\\)?
a \\(6^6\\)
12
c \\(6^{\frac{2}{3}}\\)
d \\(6^5\\)
e \\(6^{\frac{3}{2}}\\)
hiset mp 16-03

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, $n = 3$ (the index of the cube root) and $m = 2$ (the exponent of the base inside the radical), and the base $a = 6$.

Step2: Apply the rule to the given expression

Substitute $n = 3$, $m = 2$, and $a = 6$ into the formula $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. So, $\sqrt[3]{6^2}=6^{\frac{2}{3}}$.

Answer:

C. $6^{\frac{2}{3}}$