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Math Basics: Calculating and Using Exponents

By Keren Perles

What is an exponent anyway? How can you use one? This tutorial will explain how to calculate exponents and when to use them.

Calculating Exponents

There are two parts of an exponent: the base and the power. In the exponent 2^3, 2 is the base and 3 is the power. An exponent is simply a number multiplied by itself a certain number of times. For example, in the exponent 2^3, the base number 2 is multiplied by itself. The power tells you how many times to multiply the two: three times. Therefore, 2^3 is the same thing as 2 X 2 X 2, which equals 8.

Common Uses of Exponents

There are several instances in which you might use an exponent. Perhaps the most basic of these instances are area and volume calculations. To calculate the area of a square, you would multiply its length by its width. Because these two values are the same (all sides of a square are equal), you would be multiplying a number by itself – or squaring it. Therefore, if the side of the square were 8 inches, you would calculate the area by calculating 8^2, or 8X8. In other words, if you wanted to fill a square floor with tiles, and each side of the floor was 8 tiles long, There would be 8^2 = 8 X 8 = 64 tiles on the floor.

The same idea would hold true when calculating volume. You can calculate the volume of a cube by multiplying its length, times its width, times its height. If the side of a cube were 8 inches, the volume of the cube would therefore by 8^3, or 8 X 8 X 8.

Scientific Notation

Exponents are also used in scientific notation. For example, let’s say you wanted to write out the number 30,000,000,000,000. That’s a big number, and a lot of zeroes! You can make the number easier to understand, if you remember an important fact about the number 10 and exponents. If an exponent has the number 10 as its base, the exponent is just a 1 with the same number of 0’s as the power. For example, the exponent 10^5 is just a 1 with five 0’s after it, or 100,000. Therefore, instead of writing 200,000, you could just write 2 X 10^5. And instead of writing 30,000,000,000,000, you could just write 3 X 10^14. That’s still a big number, but it’s much simpler to understand!

Exponents are important, especially as you begin learning higher-level math concepts. Understanding the power of an exponent can help you through algebra, geometry, and even calculus!