Dividing Exponents

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 2÷ 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.

Dividing exponents Simplify 1
You can simplify this expression since both terms have the same base of 4.

2) Simplify 27/2-2.

Dividing exponents simplify 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.

Dividing exponents simplify 3
You can divide 12 by 4. You can also simplify x8/xsince both terms have the same base of x. 

4) Simplify x2y7/x2y-5.

Dividing exponents simplify 4
You can simplify x2/x= x0 since both terms have the same base of x. Note that anything raised to the power of zero equals 1. For example, xequals 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.

Dividing exponents simplify 6
You can simplify x5/xsince both terms have the same base of x. You can simplify y8/ysince both terms have the same base of y. You can also simplify z9/z since both terms have the same base of z.

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.

Here’s more information on exponents…
Rules of Exponents
Multiplying Exponents
Negative Exponents