## 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 5^{4}. 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, 5^{4} = 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: 6
^{0}= 1;*x*^{0}= 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: 6
^{1}= 6,*x*^{1}=*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: -2
^{2}= -2 ✕ -2 = 4; -2^{3}= -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.***