## Simplifying exponents

How to simplify exponents.

- Simplifying rational exponents
- Simplifying fractions with exponents
- Simplifying negative exponents
- Simplifying radicals with exponents

## Simplifying rational exponents

The base b raised to the power of n/m is equal to:

*b*^{n/m} = (
^{m}√*b*)* ^{n}= ^{m}√*(b

*)*

^{n}Example:

The base 2 raised to the power of 3/2 is equal to 1 divided by the base 2 raised to the power of 3:

2^{3/2} = ^{2}*√*(2^{3}) = 2.828

## Simplifying fractions with exponents

Fractions with exponents:

(*a / b*)* ^{n}* =

*a*/

^{n}*b*

^{n}Example:

(4/3)^{3} = 4^{3 } / 3^{3} = 64 / 27 = 2.37

## Simplifying negative exponents

The base b raised to the power of minus n is equal to 1 divided by the base b raised to the power of n:

*b ^{-n}* = 1 /

*b*

^{n}Example:

The base 2 raised to the power of minus 3 is equal to 1 divided by the base 2 raised to the power of 3:

2^{-3} = 1/2^{3} = 1/(2⋅2⋅2) = 1/8 = 0.125

## Simplifying radicals with exponents

For radical with exponent:

(^{m}√*a*)^{n} = *a*^{n/m}

Example:

(√5)^{4} = 5^{4/2} = 5
^{2} = 25