How to Divide Powers: 7 Steps (with Images)

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How to Divide Powers: 7 Steps (with Images)
How to Divide Powers: 7 Steps (with Images)

Dividing expressions that involve powers is much simpler than it sounds: as long as they have the same base, just subtract the exponents and rewrite the expression. Some cases require a little more attention and need a few more operations to get a final answer. Learn below the details for dividing different cases of expressions that involve powers.


Part 1 of 2: Understanding the Basics

Divide Exponents Step 1

Step 1. Write down the problem

The simplest form of power division you can find is the expression mThe ohB, where a and b are any exponents. To illustrate how a power division works, let's divide m8 finally2. To start, write the expression.

Divide Exponents Step 2

Step 2. Subtract the second exponent from the first

In the example, the second exponent is 2 and the first exponent is 8. So rewrite the problem as m8-2.

Divide Exponents Step 3

Step 3. Write the final answer

Since the result of subtraction 8 - 2 is 6, the new exponent of the expression will be 6. If the base of the potency is a number and not a variable, you could still develop the potency and solve the multiplications needed to give the final answer (for example, 24 = 2 x 2 x 2 x 2 = 16).

Part 2 of 2: Advanced Operations

Divide Exponents Step 4

Step 1. Make sure that each power of the expression has the same base

If the bases of the expression are different, it will not be possible to split it. Here are other details you need to understand:

  • If the expression has different variables as power bases, such as m6 ÷ x4, it will not be possible to simplify it.
  • If the bases of the expression are numbers rather than variables, it may be possible to work the expression so that they are the same. For example, in division 23 ÷ 41, we can see that the power of the denominator, 41, can be rewritten as 2². Thus, when replacing this other form in the expression we will have: 2³ ÷ 2² = 23-2 = 21 = 2. Be aware that this simplification is only possible when the major base can be rewritten so that it becomes a power with base equal to the minor base power of the expression.
Divide Exponents Step 5

Step 2. Split expressions from multiple variables

If the expression you are working on has multiple variables, divide each power of the numerator by the corresponding base power in the denominator. Take a look at the steps in the example below to better understand:

  • Example: x6y33z² x4y³z = x6-4y3-3z2-1 = x²y0z1 = x²z.
Divide Exponents Step 6

Step 3. Divide expressions with coefficients (ie, involving variables and numbers)

As long as the bases are the same, there will be no major problem in simplifying this type of division. You must work with the variables and the numbers separately: divide the variables as you normally do (subtracting the exponents from the powers of equal base), and then divide the numerical coefficients. Look at the example to better understand this process:

  • Example: 6x4 ÷ 3x2 = 6/3 * x4-2 = 2 * x2 = 2x2.
Divide Exponents Step 7

Step 4. Divide expressions with negative exponents

In this case, it is only necessary to move the negative exponent power to the other side of the fraction and change its sign: for example, if we have 3-4 as the numerator of a fraction, if we move this power to the denominator, it must be rewritten with positive exponent, that is, 34. Then, just use the steps already learned to simplify the expression in question. Note the following two examples:

  • Example 1: x-3/x-7 = x7/x3 = x7-3 = x4.
  • Example 2: 3x-2y/xy = 3y/(x2*xy) = 3y/(x3y) = 3/x3.


  • If you have a calculator, it's always a good idea to use it to check your answer. Repeat the arithmetic operations done throughout the simplification and check if the result is the same as what you did.
  • Don't worry if you don't get it right the first time. Keep trying until you get it.

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