Exponent Calculator

This Fabulous e calculator helps you to find the solution to an Exponential form of expression. You can find Positive as well as Negative exponents using our Raised to the power calculator. Below we will discuss What are exponents and exponents calculators? How do you calculate the exponents/power of the base manually and as well as with our exponential calculator?

What are Exponents?

Exponents are powers that are raised in the upper corner on the right side of the base exponents. They represent the no of multiplications or divisions needed to perform to simplify the expression. Exponents are of different types. They can be fraction, complex, irrational, or positive whole numbers.

Types of Exponents

Exponents are divided into two types on the basis of their nature.

When the power of the expression is positive numbers, it is said to be a positive exponent. It tells how many times a base is to be multiplied by itself.

e.g   2⁴ = 2 x 2 x 2 x 2

When the power of the expression is negative in nature, it is often said to be a negative exponent. It indicates the number of reciprocals of base required to be multiplied by itself. Simplify such Fractions with our exponent's calculator.

e.g   2^-4 = 12 x 12 x 12 x 12

How to solve Exponents by hand?

When exponents are small integers, they can be easily calculated manually.

Calculate the value of expression 5 raised to the power of 4. ( 5 to power 4)

It means 5⁴.
5 * 5 * 5 * 5 = 625
5 to the power 4 = 625
Hence the exponent is 625.

Find the solved value of exponential expression 3^-3.

It shows 13 x 13 x 13.

13 x 13 x 13 = 127.

127 = 0.037037037.

Hence the exponent is 0.037037037

Below are some solutions to commonly used exponential expressions.

Rules of Exponents:

There are some rules which apply to the exponents.

• Negative Property:

  b^-n = 1b

  Example:
  Solve  24^-2.

  Solution:
  24^-2 =  2 x14^-2

  = 2 x 4⁴
  = 2 x 16
  = 32

• Product Property:

  (b^m)(bⁿ) = b^{m + n}

  Example:
  Simplify   x³. x

  Solution:
  x³ . x  =  x³⁺¹
   = x⁴

• Quotient Property:

  b^mb^m = b^m-n

  Example:
   Find the value of 2³2.

  Solution:
  2³2 = 2^3-1
  = 2²
  = 4

• Power of a power:

  (b^a)ⁿ = b^{a x n}

  Example:
  Solve   (2³)²

  Solution:
  (2³)² = 2^3x2
  = 2⁶
  = 64

• Power of a product:

  (a b)ⁿ = aⁿ bⁿ

  Example:
    Simplify (2 x 3)²

  Solution:
  (2 x 3)² = 2² x 3²
  = 4 x 9
  = 36

• Power of a Quotient property:

  (ab)ⁿ = aⁿbⁿ

  Example:
    Find the value of   (67)².

  Solution:
  (67)² = 6²7²
  =3649