How to divide mononomies with exponents: 7 steps

2024 Author: Samantha Chapman | [email protected]. Last modified: 2023-12-17 09:13

Dividing monomials with exponents is easier than it seems. When you work with the same base, all you have to do is subtract the values of the exponents from each other and keep the same base. Here's how to proceed.

Steps

Part 1 of 2: Understanding the Basics

Step 1. Write down the problem

The simplest version of this problem will be in the form of m^to ÷ m^b. In this case, you are working with problem m⁸ ÷ m². Write it down.

Step 2. Subtract the second exponent from the first

The second exponent is 2 and the first is 8. So, you can rewrite the problem as m^{8 - 2}.

Step 3. Write your final answer

Since 8 - 2 = 6, the final answer is m⁶. It's that simple. If you are not working with a variable and you have a number as a base, for example 2, then you will have to do the math (2⁶ = 64) to solve the problem.

Part 2 of 2: Go further

Step 1. Make sure each expression has the same base

If you are working with different bases, exponents cannot be divided. Here's what you need to know:

• If you are working with a problem with variables like m⁶ ÷ x⁴, then there is no rule to simplify it.

• However, if the bases are numbers and not variables, you may be able to manipulate them so that you end up with the same base. For example, in problem 2³ ÷ 4¹, you must first make both bases "2". All you do is rewrite 4 as 2² and do the calculations: 2³ ÷ 2² = 2¹, i.e. 2.

  You can only do this, however, if you can transform the larger base into an expression of a squared number to make it the same base as the first

Step 2. Divide monomials with multiple variables

If you have an expression with multiple variables, then you just need to divide the exponents by each similar base to get the final answer. Here's how it's done:

• x⁶y³z² ÷ x⁴y³z =
• x^6-4y^3-3z^2-1 =
• x²z

Step 3. Divide monomials with numerical coefficients

While you are working with the same base, it is not a problem if each expression has a different coefficient. Just divide the exponents as you normally would and divide the first coefficient by the second. That's how:

• 6x⁴ ÷ 3x² =
• 6 / 3x^4-2 =
• 2x²

Step 4. Divide monomials with negative exponents

To divide expressions with negative exponents, all you have to do is move the base to the other side of the fraction line. So, if you have 3^-4 to the numerator of a fraction, you will have to move it to the denominator. Here are two examples:

• Example 1:

  • x^-3/ x^-7 =
  • x⁷/ x³ =
  • x^7-3 =
  • x⁴

• Example 2:

  • 3x^-2y / xy =
  • 3y / (x² * xy) =
  • 3y / x³y =
  • 3 / x³

  Advice

  • If you have a calculator, it's usually a good idea to check your answer. Compare the result with your answer to make sure they match.
  • Don't worry if you're wrong! Keep trying!