**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^{8 }÷ 2^{6 }= 2^{8-6} = 2^{2}

For example, you can simplify 2^{8} ÷ 2^{6} since both terms have the same base, which is 2. Here are some more examples of dividing exponents.

1) Simplify 4^{9}/4^{6}.

You can simplify this expression since both terms have the same base of 4.

2) Simplify 2^{7}/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 12x^{8}/4x^{3}.

You can divide 12 by 4. You can also simplify x^{8}/x^{3 }since both terms have the same base of x.

4) Simplify x^{2}y^{7}/x^{2}y^{-5}.

You can simplify x^{2}/x^{2 }= x^{0} since both terms have the same base of x. Note that anything raised to the power of zero equals 1. For example, x^{0 }equals 1. You can also simplify y^{7}/y^{-5 }since both terms have the same base of y.

5) Simplify x^{2}y^{2}/z^{2}.

You cannot simplify this expression because the bases x, y and z are not the same.

6) Simplify 7x^{5}y^{8}z^{9}/x^{2}y^{3}z.

You can simplify x^{5}/x^{2 }since both terms have the same base of x. You can simplify y^{8}/y^{3 }since both terms have the same base of y. You can also simplify z^{9}/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 z^{1}.

You have now learned what to do when dividing exponents.

*Here’s more information on exponents…*

* Rules of Exponents*

*Multiplying Exponents*

* Negative Exponents*