Let’s discuss the rule you need to know when dividing exponents. Understanding this basic rule will help you simplify algebra problems you come across.
Dividing Exponents Rule: When dividing numbers or variables with the same base, you can just subtract the exponents. The number to the left of an exponent is called the base.
Base 28 ÷ 26 = 28-6 = 22
For example, you can simplify 28 ÷ 26 since both terms have the same base, which is 2. Here are some more examples of dividing exponents.
1) Simplify 49/46.
2) Simplify 27/2-2.
You can simplify this expression since both terms have the same base of 2. Note that when subtracting, if two negative (-) signs appear side by side, you can replace them with a single plus sign (+). For example, 7 – (-2) equals 7 + 2.
3) Simplify 12x8/4x3.
4) Simplify x2y7/x2y-5.
You can simplify x2/x2 = x0 since both terms have the same base of x. Note that anything raised to the power of zero equals 1. For example, x0 equals 1. You can also simplify y7/y-5 since both terms have the same base of y.
5) Simplify x2y2/z2.
You cannot simplify this expression because the bases x, y and z are not the same.
6) Simplify 7x5y8z9/x2y3z.
Note if an exponent does not appear beside a variable, such as z, you can assume the exponent is 1. For example, z equals z1.
You have now learned what to do when dividing exponents.