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What are the Basic Laws of Exponents?

Updated on April 16, 2012

Basics of Exponents

An exponent is the superscript number that appears in the upper right corner above the base number. This number indicates how many times a base number should be multiplied by itself.

y2 = y × y

b5 = b x b x b x b x b

73 = 7 x 7 x 7

6 x 6 x 6 x 6 = 64

Negative Exponent

negative exponent
negative exponent | Source

Negative Exponents

A negative exponent indicate that we will be dealing with the reciprocal of the number with the position version of the exponent.


Fractional Exponents

An exponent that is a fraction instead of an integer is called a Fractional Integer

Multiply Powers of the Same Number

To multiply powers of the same base you add the exponents.

bn × bm = bn+m


Division of Powers with the Same Base

To divide powers of the same base you simply subtract the exponents.


Power of 1

Any number with the power of 1 is equal to itself

a1 = a

51 = 5

Proof for the Exponenet Power of Zero


Power of 0

The power of zero is equal to 1. This is known as the zero exponent rule.

a0 = 1

650 = 1


using the law of division for exponents

Looking at the equation to the right we see that bm-m = b0 = 1


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    • Taleb80 profile image

      Taleb AlDris 5 years ago

      Thanks for sharing this useful hub.

      I voted useful & Up.