Exponent \((a^b)\) Calculator

Lets first understand, what are exponent and how we can calculate the exponent?

Exponentiation

Exponentiation is a mathematical operation, written as a^b, involving two numbers, the base a and the exponent b, and pronounced as "a raised to the power of b".

\[ a^b=a*a*a*\cdots*a\smash{\llap{\underbrace{\phantom{a*a*a*\cdots*a}}_{\text{$b$ times}}}}\]

When b is a positive integer, exponentiation corresponds to repeated multiplication of the base a that is, a^b is the product of multiplying a bases.

The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices.

Exponentiation is used extensively in many fields, including economics, physics, computer science with applications such as compound interest, population growth, chemical reaction kinetics, and public-key cryptography.

Basic Laws of Exponentiation

Zero exponent

\(a^{0}=1\)

Ex: \(5^{0}=1\)

Negative exponent

\(a^{-n}=\dfrac{1}{a^n}\)

Ex: \(5^{-2}=\dfrac{1}{5^2}=\dfrac{1}{25}=0.04\)

Positive exponent

\(a^{m+n}=a^m.a^n\)

Ex: \(5^{3+2}=5^3.5^2=125*25=3125\)

\((a.b)^m=a^m.b^m\)

Ex: \((2.5)^{2}=2^2.5^2=4.25=100\)

\(a^{m-n}=\dfrac{a^m}{a^n}\)

Ex: \(5^{3-2}=\dfrac{5^3}{5^2}=\dfrac{125}{25}=5\)

\((a^m)^n=a^{m.n}\)

Ex: \((2^5)^{2}=2^{10}=1024\)

For calculating exponents using above exponent calculator, you have to just write the base and the exponent in the given input boxes and press the calculate button, you will get the result.