In mathematics, exponents are algebraic expression usually written in the form C^x , where āCā is the base and āxā is the exponent. It is an easier way to express expressions that have repeated multiplication.

For example, it is less cumbersome to write 8^4 than 8_8_8*8. When a student is unfamiliar with the rules of exponents, it may be a difficult task to simplify exponential expressions. Although there are a few rules for exponents, some students may have problems with the division properties of exponents. With this tutorial, you can easily learn to apply the division properties of exponents.

Understand how to apply the division property of exponents to simplify exponential expressions properly. One law of exponents, called the quotient rule, states that to perform a division of two exponential expressions, the expressions must have the same base. When dividing such expressions, subtract the exponent that is in the denominator from the exponent that is in the numerator.

Apply this rule to the exponential expressions C^x /C^y and they become C^(x-y ). Evaluate the expression C ^(x-y ) to solve an exponential problem with one variable (C).

Use the same rule from Step 2 to evaluate expressions with multiple variables such as (C^x X D^z )/ (C^y X D^t ). Utilizing the division properties of exponents to simplify these exponential expressions, you find that the expressions become [C^(x-y)] * [D^(z-t )].

Learn to simplify exponential expressions with the quotient rule by using the example: [(8^ 7) * (4^ 4) * (5^ 8)] / [(8^ 6) * (4^2) * (5^ 5)]

Utilize the rule from Step 3 to get that [(8^(7-6)) * (4^ (4-2)) * 5^ (8-5)] = [(8^1) * (4^ 2) * (5^3 )].

Evaluate the expression [(8^1) * (4^ 2) * (5^3 )] to solve completely this exponential problem. By multiplying each number in the expression, you find that [(8^1) * (4^ 2) * (5^3 )] = 8_16_125= 16000. Alternatively, use an online calculator to perform this calculation or to check the answer (see the Resource section).

#### Tip

When you divide exponents, it is important to remember the correct order in which to subtract the exponents of an exponential expression.

For the other properties that pertain to exponents, such as power and product rules, see the Resource section.