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Bond [772]
3 years ago
14

How to right a radical in exponential form

Mathematics
1 answer:
Law Incorporation [45]3 years ago
3 0

Answer:

  \sqrt[n]{x}=x^{\frac{1}{n}}

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:

\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

That is ...

\sqrt[3]{x}=x^{\frac{1}{3}} \quad\text{radical index = fraction denominator}

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