   # Using Exponents

 Our Pre-Algebra tutorial software program contains over 60 topic areas. One of them is Using Exponents, and this page summarizes the main ideas of this topic. This page is intended for review, and is not a substitute for the interactive, self-paced tutorials of the MathTutor pre-algebra software program.

General Explanation

In mathematics, you will soon come across many long ways of doing things and many shortcuts that accomplish the same thing. In this lesson we will see how to simplify how we write an expression by using something called an EXPONENT.

Look at this multiplication: 7 x 7 x 7 x 7

There are four factors, and each has a value of 7. This can be written as 74. The "7" is called the base and the "4" is called the exponent. The exponent tells how many times the base is used as a factor. The entire expression "74" is called a power.

In general, rn = {r x r x r x r ..... x r} with r as a factor n times.
```s1 = s = "5 to the first power"
s2 = s x s = "5 to the second power"
s3 = s x s x s = "5 to the third power"
```
Two other important facts about exponents are:
```a1 = a: any number to the "1" power is itself
a0 = 0: any number to the "0" power is 1```
Exponents of positive two and three have special names: SQUARES and CUBES, respectively.
```92 = "9 squared"
53 = "3 cubed"
```
Sample Problem

Find the value of the following:
```93 = ?
```

Solution

Since the base is 9 and the exponent is 3, we must use 9 as a factor three times.

```9 x 9 x 9 = 729

The value of 93 is 729
```