# Exponential Power Calculator

Calculate the exponential power for given values:
 Base (a): Exponent (n):

 Result :
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 FormulaExample
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$$x^{m/n} = \sqrt[n]{x^m} = (\sqrt[n]{x})^m$$$$4^{3/2} = (\sqrt{4})^3=2^3=8$$