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# What are the Basic Laws of Exponents?

## 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.

y^{2} = y × y

b^{5} = b x b x b x b x b

7^{3} = 7 x 7 x 7

6 x 6 x 6 x 6 = 6^{4}

## Negative Exponent

## 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.

b^{n }× b^{m} = b^{n+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

**a ^{1} = a**

**5 ^{1} = 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

WHY??

using the law of division for exponents

Looking at the equation to the right we see that b^{m-m} = b^{0 }= 1