Question

Why does cube root 7 equal 7 to the 1/3 power

Answer 1

Answer:

Step-by-step explanation:

Here's how you convert:

$\sqrt[n]{x^m}=x^{\frac{m}{n}$  The little number outside the radical, called the index, serves as the denominator in the rational power, and the power on the x inside the radical serves as the numerator in the rational power on the x.

A couple of examples:

$\sqrt[3]{x^4}=x^{\frac{4}{3}$

$\sqrt[5]{x^7}=x^{\frac{7}{5}$

It's that simple. For your problem in particular:

$\sqrt[3]{7}$ is the exact same thing as $\sqrt[3]{7^1}=7^{\frac{1}{3}$