Question

1. express $sqrt3{8}$ as an exponent:

a. $3^8$
b. $4$
c. $8^3$
d. $8^{\frac{1}{3}}$

Explanation:

Step1: Recall the radical to exponent rule

The rule for converting a radical to an exponent is that $\sqrt[n]{a}=a^{\frac{1}{n}}$, where $n$ is the index of the radical and $a$ is the radicand.

Step2: Apply the rule to $\sqrt[3]{8}$

Here, the index $n = 3$ and the radicand $a=8$. So, using the rule $\sqrt[n]{a}=a^{\frac{1}{n}}$, we substitute $n = 3$ and $a = 8$ to get $\sqrt[3]{8}=8^{\frac{1}{3}}$.

Answer:

d. $8^{\frac{1}{3}}$