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.
You should learn the rules for basic operations involving exponents. Here are the rules involving division:
- To divide one exponential term by another, keep the base the same and subtract the exponent in the denominator from the exponent in the numerator: xy/xz = xy − z
Example: 25/23 = 25 - 3 = 22 = 4
- When two terms in a division problem (in other words, a fraction) have the same exponent, apply the exponent to each: (x/y)z = xz/yz
Example: (2/3)2 = 22/32 = 4/9