## 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)(b^{n}=^{m}√)^{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= 1 /^{-n}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) = 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

## See also