# 7.2 Skills Practice Division Properties of Exponents

Exponents are mathematical expressions that represent repeated multiplication. In other words, an exponent is a shorthand way of expressing a number raised to a certain power. For example, the expression x⁴ means that x is to be multiplied by itself four times. This can also be written as x × x × x × x.

When two expressions contain exponents that are the same, they can be divided using the same properties as when two expressions with no exponents are divided. The key to properly dividing two expressions with exponents is to understand the rules of exponents. This can be done by understanding the rules of multiplication and division and how they apply to exponents.

## Rules of Exponents When Dividing

When two exponents are divided, the following rules apply: the base of the dividend (the number being divided) is kept the same, and the exponent of the dividend is subtracted from the exponent of the divisor (the number doing the dividing). For example, if you had the expression x⁴/x², the result would be x² because the base (x) is kept the same, and the exponent of the dividend (4) is subtracted from the exponent of the divisor (2) to get the result of 2.

The same rules apply when more than two exponents are divided. The base of the dividend is kept the same, and the exponents of the dividend are subtracted from the exponents of the divisor. For example, if you had the expression x⁴/x²/x³, the result would be x because the base (x) is kept the same, and the exponents of the dividend (4 and 2) are subtracted from the exponent of the divisor (3) to get the result of 1.

## 7.2 Skills Practice Division Properties of Exponents

To practice using the rules of exponents when dividing, complete the following 7.2 Skills Practice Division Properties of Exponents worksheet. This worksheet contains 10 problems that involve dividing two or more expressions that contain exponents. Complete each problem by applying the rules of exponents when dividing. Once you have finished the worksheet, check your answers to make sure you have correctly applied the rules of exponents.

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Dividing expressions with exponents requires understanding the rules of exponents when dividing. This can be done by understanding the rules of multiplication and division and how they apply to exponents. To practice using the rules of exponents when dividing, complete the 7.2 Skills Practice Division Properties of Exponents worksheet. Make sure to check your answers to ensure you have correctly applied the rules of exponents.