## Dividing 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.

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:
*x*/^{y}*x*=^{z}*x*^{y}^{− z}

**Example**: 2^{5}/2^{3}= 2^{5 - 3}= 2^{2}= 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}*x*/^{z}*y*^{z}

**Example**: (2/3)^{2}= 2^{2}/3^{2}= 4/9