# 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 calculator? How do you calculate 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 a fraction, complex, irrational, or positive whole numbers.

## Types of Exponents

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

Positive:

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

Negative:

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 to itself. Simplify such Fractions with our exponents 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.

Example:1

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

Solution:

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

Example:2

Find the solved value of exponential expression 3-3.

Solution:

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.

 0.1 to the power of 3 0.00100 0.5 to the power of 3 0.12500 0.5 to the power of 4 0.06250 1.2 to the power of 4 2.07360 1.02 to the 10th power 1.21899In-Depth 1.03 to the 10th power 1.34392 1.2 to the power of 5 2.48832 1.4 to the 10th power 28.92547 1.05 to the power of 5 1.27628 1.05 to the 10th power 1.62889 1.06 to the 10th power 1.79085 2 to the 3rd power 8 2 to the power of 3 8 2 raised to the power of 4 16 2 to the power of 6 64 2 to the 7th power 128 2 to the 9th power 512 2 to the 10th power 1024 2 to the 15th power 32768 2 to the 10th power 1024 2 to the power of 28 268435456 3 to the power of 2 9 3 to the 3 power 27 3 to the 4 power 81 3 to the 8th power 6561 3 to the 9th power 19683 3 to the 12th power 531441 2 to the power of 5 32 3 to what power equals 81 34 4 to the power of 3 64 4 to the power of 4 256 4 to the power of 7 16384 7 to the power of 3 343 12 to the 2nd power 144 2.5 to the power of 3 15.625 12 to the power of 3 1728 10 exponent 3 1000 24 to the second power (242) 576

## 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:

(bm)(bn) = bm + n

Example:
Simplify   x3 . x

Solution:
x3 . x  =  x3+1
= x4

• Quotient Property:

bmbm = bm-n

Example:
Find the value of 232.

Solution:
232 = 23-1
= 22
= 4

• Power of a power:

(ba)n = ba x n

Example:
Solve   (23)2

Solution:
(23)2 = 23x2
= 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

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