Question

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

Answer 1

Explanation:

Here's how you convert:

`\sqrt[n]{x^m}=x^{(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^{(4)/(3)`

`\sqrt[5]{x^7}=x^{(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^{(1)/(3)`