Simplifying exponents

How to simplify exponents.

Simplifying rational exponents

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

bn/m = (mb)n = m(bn)

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:

23/2 = 2(23) = 2.828

Simplifying fractions with exponents

Fractions with exponents:

(a / b)n = an / bn

Example:

(4/3)3 = 43 / 33 = 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 / bn

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 = 1/23 = 1/(2򈭾) = 1/8 = 0.125

Simplifying radicals with exponents

For radical with exponent:

(ma)n = an/m

Example:

(√5)4 = 54/2 = 52 = 25

 


See also

Write how to improve this page