#### Powers: Definition and Simple Powers with Numbers

Even though you may not be aware of it, you have already encountered the concept of “raising a number to a power”. Consider the following simple example:

3 × 3 = 9

We can re-write this as: 3^{(2)}=9

This notations simply means that if we take the number 3 and multiply it by itself we get 9. Let us consider:

3 × 3 × 3 = 3^{(3) = 27. This means that three threes multiplied together gives us 27.}

In the above examples we say that the number 3 is *raised to a power*. If 3 is raised to the 2nd power, we get 9 and if 3 is raised to the 3rd power we get 27. In fact, writing the number of times that we multiply something into itself as a *power* – with the notation of the power as being a superscript to the right of the number – can save us quite a lot of space!. Suppose we were multiplying 3 by itself 6 times, and compare the following:

3x3x3x3x3x3 = 729

3^{6} = 729

Clearly, the 2nd way of writing has the advantages of: (i) being more efficient and (ii) being easier to see how many times the number is being multiplied into itself. Futhermore, as you will see below, this way of indicating numbers and powers makes the algebraic manipulation of numbers and multiplication of large values much much easier.

re-posted from lasp.colorado.edu

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