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Negative Exponent Examples and Basics

Q:  What is a negative exponent?  What does a negative exponent do?

A:  A negative exponent is just notation that can be used to represent a reciprocal.  Let me show you some examples:

x – 1 = 1/x1 or 1/x

x-2 = 1/x2

4 – 1 = 1/41 or 1/4

4 – 2 = 1/42 = 1/16

Those are the basics.  Let’s look at a few more complicated examples of how negative exponents affect an expression:

3x – 4 = 3/x4

4x6y – 3 = 4x6/y3

OR… If the negative exponent is affecting something in a denominator, it will move it to the numerator like so:

1/x – 5 = 1*x5 = x5

6/y – 7 = 6y7

These are just a few basic examples to show you how negative exponents work. Of course things can get more difficult.

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Fractional Exponents

Q:  What does it mean when you have a fraction as an exponent?

A:  Firstly, we must be familiar with the following: Xa/b = b√Xa

When rewriting, think of a fractional exponent as a “tree”. The top number is the number of branches (how many multiples of X there are) and the bottom number is the root. Continue reading Fractional Exponents