Question

delcie is asked to rewrite the expression \\(\sqrt3{500}\\) using an exponent.

how should delcie correctly rewrite the expression?

\\(\bigcirc\\) \\(500^3\\)

\\(\bigcirc\\) \\((\sqrt3{500})^3\\)

\\(\bigcirc\\) \\((\sqrt3{500})^{\frac{1}{3}}\\)

\\(\bigcirc\\) \\(500^{\frac{1}{3}}\\)

Explanation:

Step1: Identify the radical expression

$$\sqrt[3]{500}$$

Step2: Apply the rational exponent rule

$$\sqrt[n]{x} = x^{\frac{1}{n}}$$

Step3: Rewrite the expression

$$500^{\frac{1}{3}}$$

Answer:

\(500^{\frac{1}{3}}\)