Simplifying exponents

How to simplify exponents.

Simplifying rational exponents

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

b^n/m = (^m√b)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:

2^3/2 = ²√(2³) = 2.828

Fractions with exponents:

(a / b)ⁿ = aⁿ / bⁿ

Example:

(4/3)³ = 4³ / 3³ = 64 / 27 = 2.37

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⋅2⋅2) = 1/8 = 0.125

For radical with exponent:

(^m√a)ⁿ = a^n/m

Example:

(√5)⁴ = 5^4/2 = 5^² = 25