How to Divide Powers: 7 Steps (with Pictures)

2024 Author: Jason Gerald | [email protected]. Last modified: 2023-12-16 10:50

Dividing numbers to exponents is actually not as complicated as you might think. As long as the bases are the same, all you have to do is subtract the power of the number and keep the base the same. If this is difficult to understand, start reading Step 1 for an easy guide to dividing numbers by powers.

Step

Part 1 of 2: Understanding the Basics of Division of Powers

Step 1. Write down the questions

The simplest version of this problem is of the form m^a m^b. In this form, for example, you work on the problem m⁸ m². Write down the question.

Step 2. Subtract the power of the second number from the power of the first number

The power of the second number is 2, and the power of the first number is 8. So, rewrite the problem as m^8-2.

Step 3. Write down the final answer

Since 8 - 2 = 6, the final answer is m⁶. As simple as that. If the base is a number, not a variable, then the final answer must be calculated (for example, 2⁶ = 64) to solve the problem.

Part 2 of 2: Understanding More

Step 1. Make sure every number has the same base

If the bases are different, division cannot be performed. Here's what you need to know:

• If the question is a variable, for example m⁶ x⁴, then nothing else can be done to simplify it.

• However, if the base is a number, you may be able to manipulate the numbers to the power of making them have the same base. For example, in problem 2³ ÷ 4¹, you have to make both bases "2" first. All it has to do is change 4 to 2², and calculate: 2³ ÷ 2² = 2¹, or 2.

  However, this method can only be done if the larger base can be converted to a power number with the same base as the base of other power numbers in the problem

Step 2. Calculate division to the power of multiple variables

If the question has multiple variables, just divide the variables to the power of the same base to get the final answer. Here's how:

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

Step 3. Calculate the division of the variable to the power of the coefficient

As long as the bases are the same, it doesn't matter even if the exponent variables have different coefficients. Just divide the variable to the power as usual, and divide the first coefficient by the second coefficient. Here's how:

• 6x⁴ 3x² =
• 6/3x^4-2 =
• 2x²

Step 4. Calculate the division of the variable to the negative exponent

To divide a variable to a negative exponent, all you have to do is move the base to the opposite side of the fraction line. So, if 3^-4 is in the place of the numerator of the fraction, move it to the place of the denominator. Here are two examples of questions about this:

• Example 1:

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

• Example 2:

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

Tips

• Don't be afraid to be wrong! Keep trying!
• If you have a calculator, double-check your answers. Calculate manually or with a calculator to ensure the result remains the same.