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The Basics of Working with Exponents

Exponents (also called powers) are shorthand for repeated multiplication. For example, 23 means to multiply 2 by itself three times. To do that, use the following notation:

image0.jpg

In this example, 2 is the base number and 3 is the exponent. You can read 23 as “2 to the third power” or “2 to the power of 3” (or even “2 cubed,” which has to do with the formula for finding the value of a cube).

Here’s another example:

105 means to multiply 10 by itself five times

That works out like this:

image1.jpg

This time, 10 is the base number and 5 is the exponent. Read 105 as “10 to the fifth power” or “10 to the power of 5.”

When the base number is 10, figuring out any exponent is easy. Just write down a 1 and that many 0s after it:

1 with two 0s 1 with seven 0s 1 with twenty 0s
102 = 100 107 = 10,000,000 1020 = 100,000,000,000,000,000,000

Exponents with a base number of 10 are important in scientific notation.

The most common exponent is the number 2. When you take any whole number to the power of 2, the result is a square number. For this reason, taking a number to the power of 2 is called squaring that number. You can read 32 as “three squared,” 42 as “four squared,” and so forth. Here are some squared numbers:

image2.jpg

Any number (except 0) raised to the 0 power equals 1. So 10, 370, and 999,9990 are equivalent, or equal, because they all equal 1.

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