Answer:
[tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]
Step-by-step 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:
[tex]\sqrt[3]{x}\cdot \sqrt[3]{x}\cdot \sqrt[3]{x}=(\sqrt[3]{x})^3=x\\\\(x^{\frac{1}{3}})^3=x^{\frac{3}{3}}=x^1=x[/tex]
That is ...
[tex]\sqrt[3]{x}=x^{\frac{1}{3}} \quad\text{radical index = fraction denominator}[/tex]
