# Exponents: Rational exponents

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##### Examples

###### Lessons

- prove: $a^{3 \over 8} = {^8}\sqrt{a^3}$
**Simplifying Expressions Using: ${^n}\sqrt{x}=x^{\frac{1}{n}}$**

Simplify the following expressions if possible.- evaluate:
**Simplifying Expressions Using: $x^{-\frac{1}{n}}=\frac{1}{x^{\frac{1}{n}}}=\frac{1}{{^n}\sqrt{x}}$**

Simplify the following expressions.**Simplifying Expressions Using: $x^{\frac{m}{n}}={^n}\sqrt{x^m}$**

Simplify the following expressions if possible.

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###### Topic Notes

• ${^n}\sqrt{x}=x^{\frac{1}{n}}$

• $x^{-\frac{1}{n}}=\frac{1}{x^{\frac{1}{n}}}=\frac{1}{{^n}\sqrt{x}}$

• $x^{\frac{m}{n}}={^n}\sqrt{x^m}$

• $x^{-\frac{1}{n}}=\frac{1}{x^{\frac{1}{n}}}=\frac{1}{{^n}\sqrt{x}}$

• $x^{\frac{m}{n}}={^n}\sqrt{x^m}$

###### Basic Concepts

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