# Exponent Calculator - Calculatorall.com

Exponents usually have two parts, the base and the exponent. Our exponent calculator works on the same principles and when you provide the value for both these parts our calculator gives you the result by multiplying the base exponent number of times.

 ^ = ?

How Exponentiation Works?

Well, it's another mathematical operation and is represented as an, where a is the base while n is the exponent. When n is some positive integer, exponentiation repeatedly multiplies the base, n number of times. Our exponent calculator also accepts the negative bases but doesn't perform the computation for imaginary numbers. It doesn't accept fractions either but you can still use it for computing the fractional exponents if you enter the exponents in decimal form.

The Basic Laws for Exponents

When the exponents sharing same base have to be multiplied, you add the exponents and keep the base same.

an * am = a(n+m)

In case of negative exponents, the base is reciprocated to remove that negative sign from the exponent while it is raised to that same exponent with positive sign.

a(-n) = 1 / an

When dividing the exponents having same base, you have to subtract the exponents and the base is kept the same.

am / an = a(n-m)

When there is another exponent above the exponent, you have to simply multiply the exponents.

(am)n = a(n-m)

When there is another exponent above the exponent, you have to simply multiply the exponents.

(am)n = a(n * m)

When the bases are multiplied and there is an exponent on top, exponent goes on top of each of the bases separatel/>
(a * b)n = an * bn

When bases are divided and there is an exponent on top, exponent goes on top of each of the bases separately.

(a / b) n = an / bn

When the exponent is the constant 1, there is no change made to the base.

a1 = a

When the exponent is the constant 0, result of exponentiation will be 1 always regardless of the base.

a0 = 1

Given below is the example of how is a0=1. The demonstration uses one of exponent laws mentioned above.

IF

an * am = a(n + m)

Then

an * a0 = a(n+0) = an

So, only way to keep an unchanged through multiplication, and to keep the exponent law true, is to keep a0 equal to 1.

How The Exponent Calculator Works?

The exponent calculator here works by following all the above mentioned exponentiation principles. It gives you two fields to enter the base and the exponent. You have to enter base in field present to left side of carat "^" sign while the exponent should go in the one to the right of that sign. After entering the values for the base and the exponent, just click the "Calculate button" and the result will be calculated for you.