Simplifying Exponents
Exponents, sometimes called “powers,” are a simple way of showing repeated multiplication. As an example, multiply five by itself four times, as in 5 ✕ 5 ✕ 5 ✕ 5. Another way to express this would be as “five raised to the fourth power,” or 54. In this example, the five is called the base and the four is called the exponent. The exponent is the number of times the base is multiplied by itself. To find the value of an exponent, simply perform the multiplication: 5 ✕ 5 = 25; 25 ✕ 5 = 125, and 125 ✕ 5 = 625. Therefore, 54 = 625.
There are a few special rules related to exponents:
- When a number is raised to the second power, we often say that it is squared.
- When a number is raised to the third power, we often say that it is cubed.
- Any number besides zero raised to the power of zero is always equal to 1: 60 = 1; x0 = 1, so long as x ≠ 0. (Zero raised to any power is, of course, equal to zero.)
- A number raised to the first power is always equal to itself: 61 = 6, x1 = x, and so on.
- When the exponent is negative, the result is a fraction with 1 in the numerator and the result of the multiplication (ignoring the negative symbol) in the denominator. For example, 3-2 = 1/9 and 5-4 = 1/625.
- When the base is negative, follow the rules for multiplying negatives: -22 = -2 ✕ -2 = 4; -23= -2 ✕ -2 ✕ -2 = -8; and so on.
*Remember, you will be able to use a calculator on the GED Math test. Your goal should be to understand why your answer is correct.*