Question

rational exponents practice
complete this assessment to review what you’ve learned. it will not count toward your grade.

what rational exponent could be used to express \\\\(\sqrt3{23}\\\\)? (1 point)

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check answer remaining attempts : 3

Explanation:

Step1: Recall the formula for radicals and exponents

The formula that relates a radical to a rational exponent is $\sqrt[n]{a}=a^{\frac{1}{n}}$, where $n$ is the index of the radical and $a$ is the radicand.

Step2: Apply the formula to $\sqrt[3]{23}$

In the expression $\sqrt[3]{23}$, the index $n = 3$ and the radicand $a=23$. Using the formula $\sqrt[n]{a}=a^{\frac{1}{n}}$, we substitute $n = 3$ and $a = 23$. So $\sqrt[3]{23}=23^{\frac{1}{3}}$.

Answer:

$\frac{1}{3}$ (as the exponent, so the rational exponent is $\frac{1}{3}$ and the expression is $23^{\frac{1}{3}}$)