What Is An Exponent?

To multiply a number by itself a certain number of times, you can show that by using an exponent. Say that you want to multiply 34 times. You can work that out this way. Three times three equals nine. Nine times three equals 27 27 times three equals 81. There are many times in solving math problems, where it is useful to multiply a number by itself a specific number of times. A simple example of this is when you have a square and you measure one of its sides. You might want to have some idea of how big the area of the square is. The formula for the area of a square is its length multiplied by its height. 10 " by 10 " is 100 square inches. One way you could write this would be using exponent notation. That is, list the base number, in this case, the ten, and the number of times you are going to multiply the base? Two. In this case, the ten is called the base, and the two is called the exponent. The exponent is also called the power. In the process of multiplying a number by itself is called squaring the number. We could read ten to the second as ten squared. But exponents don't stop here. You can multiply number by itself any number of times. Let's go one more on the square. What if we want to find the volume of a cube? The formula for the volume of a cube is the length times the width times the height. In a cube, all sides have the same length. Now, let's take all those square inches and make them cubes and run them up the height of the cube. Now we have a cube that is 10 " by 10 " by 10 ". If we turn the cube round so that we can see the back side, we can see that there are 1,000 cubes or 1,000 cubic inches. This is ten to the power of three. The base is still ten, but now the exponent is three. Rising a base to the power of three is often called cubing the base number. But we aren't limited to twos and threes when it comes to exponents. We can use any number we want. We can say five to the power of four or two to the power of seven. Or 247 to the power of 16, but we won't work that out on screen. It would take too long. There are a couple of special cases with exponents to remember. The first is that any number raised to the power of one is always itself. So, for example, two to the power of one is two. Another is that any non zero number raised to the power of zero is one. So two to the power of zero is one. Exponents are used in many places in math. They are used in geometry and algebra, and trigonometry and calculus. They are extremely useful in engineering, computer programming, medicine, science, and business. So learning how to work with them is very important.