Question

How to right a radical in exponential form

Answer 1

`\sqrt[n]{x}=x^{(1)/(n)}`

Explanation:

The index of a radical is the denominator of a fractional exponent, and vice versa. If you think about the rules of exponents, you know this must be so.

For example, consider the cube root:

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

That is ...

`\sqrt[3]{x}=x^{(1)/(3)} \quad\text{radical index = fraction denominator}`