What Does a Negative Exponent Mean?

Algebra

When exponents are whole positive numbers, the definition just seems to work and make sense. As soon as you put a negative in front of that exponent though, the meaning changes completely (ok MOSTLY is a better word here)!

x^{-n}=\dfrac{1}{x^n}

A negative exponent means to find 1 over the same thing with a positive exponent. That sounds confusing, so I’m going to show you with a couple of examples.

x^{-2}=\dfrac{1}{x^2}  

3^{-3}=\dfrac{1}{3^3}=\dfrac{1}{27} 2^{-4}=\dfrac{1}{2^4}=\dfrac{1}{16}

As you can see, it is really just shorthand, but since it comes up a lot when you are doing things in algebra or calculus it is important to know how to simplify it! The same is true for exponents which are fractions.

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2 Comments:

  1. MathBootcamps Blog » What are Exponents and What Do They Mean? @ 2011-06-03 13:52

    [...] work differently if the exponents are negative or if the exponents are [...]

  2. MathBootcamps Blog » Exponents that are Fractions @ 2011-06-03 13:58

    [...] This week, I have talked about what exponents mean when they are whole, positive numbers and what they mean when they are negative numbers. [...]

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