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