what is $sqrt3{9}$ written in exponential form?\na. $3^{-3/2}$\nb. $3^{-2/3}$\nc. $3^{1/3}$\nd…
what is $sqrt3{9}$ written in exponential form?\na. $3^{-3/2}$\nb. $3^{-2/3}$\nc. $3^{1/3}$\nd. $3^{2/3}$\ne. $3^{3/2}$
Answer
Explanation:
Step1: Rewrite the radicand
We know that $9 = 3^2$. So $\sqrt[3]{9}=\sqrt[3]{3^2}$.
Step2: Use the radical - exponent rule
The rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. Here $a = 3$, $m = 2$ and $n = 3$. So $\sqrt[3]{3^2}=3^{\frac{2}{3}}$.
Answer:
D. $3^{\frac{2}{3}}$