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Number Calculator

Exponential Power Calculator

Calculate the exponential power for given values:

Calculator to find the value of entered exponential expression using exponent formula:

aⁿ = a×a×...×a (n times)

where
a is any real number and

n is a positive integer

The basic rules for exponentiation is that base (a) is raised to the power of n, is equal to n times multiplication of a.

For example:

2 is raised to power 5

2⁵= 2 X 2 X 2 X 2 X 2 = 32

Basic rules for exponentiation

Rule	Formula	Example
Product	$x^ax^b = x^{a+b}$	$2^22^3 = 2^5=32$
Quotient	$\displaystyle \frac{x^a}{x^b} = x^{a-b}$	$\displaystyle \frac{2^3}{2^2} = 2^1 =2$
Power of power	$(x^a)^b = x^{ab}$	$(2^3)^2 = 2^6=64$
Power of a product	$(xy)^a = x^ay^a$	$36=6^2=(2 x 3)^2$ $= 2^2 x 3^2=4 x 9=36$
Power of one	$x^1=x$	$2^1=2$
Power of zero	$x^0=1$	$2^0=1$
Power of negative one	$\displaystyle x^{-1}=\frac{1}{x}$	$\displaystyle 2^{-1}=\frac{1}{2}$
Change sign of exponents	$\displaystyle x^{-a} = \frac{1}{x^a}$	$\displaystyle 2^{-3} = \frac{1}{2^3} = \frac{1}{8}$
Fractional exponents	$x^{m/n} = \sqrt[n]{x^m} = (\sqrt[n]{x})^m$	$4^{3/2} = (\sqrt{4})^3=2^3=8$