What are Exponents and What Do They Mean?

Algebra

Mathematicians LOVE to make up cool new words to describe things. Well, ok, everyone does right? It just makes life simpler!

The word “exponent” is one of those things. First of all, it refers to the number (or variable) that looks like it is floating just above another number or variable. In x^2, 2 is the exponent and in 4^{12}, 12 is the exponent. That takes care of that, but what does  x^2 or   4^{12} mean?

The exponent tells you how many times to multiply the number or the variable by itself (at least as long as it is a positive whole number it does). Some examples:

  2^3=2\cdot2\cdot2=8

  x^3=x\cdot x\cdot x (the value repends on x)

  5^2=5\cdot5=25

As you can see,   4^{12} means “4 multiplied by itself 12 times”! That’s a huge number!

There are a couple of things to note:

  • Anything with an exponent of zero is defined to be 1. So,   4^{0}=1,   100^{0}=1.
  • Ok right above, when I said anything, I meant “almost anything”. 0^0 is an indeterminate form.
  • An exponent of 1 is the same as just writing the number by itself:   4^{1}=4.
  • Things work differently if the exponents are negative or if the exponents are fractions.

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2 Comments:

  1. MathBootcamps Blog » What Does a Negative Exponent Mean? @ 2011-06-01 06:18

    [...] 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! [...]

  2. MathBootcamps Blog » Exponents that are Fractions @ 2011-06-03 13:50

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

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