# Division of Exponents Worksheets

This is a core skill in most science labs. It lays a good foundation to work with operations in scientific notation. While this is very intimidating when you first see a problem, students quickly learn that this skill is quite simple. The most difficult part of this unit is understanding integer operations especially with negative values. Remind students that subtracting a negative value by another negative makes the sign flip and it becomes a negative plus a plus. This set of worksheets and lessons help students understand how to divide values that contain exponents. We introduce binomials in this section. The math is the same, you just need to split them up and stay organized all the way through the problem.

### Aligned Standard: 8.EE.A.1

- Simple Lesson- This includes the use of negative numbers as well.
- Complex Lesson- A two dimensional problem is given (numerals and variables).
- Guided Lesson - Each problem has a different level of difficulty for you.
- Guided Lesson Explanation - We practice using the quotient rule over the series.
- Simple Quotients of Exponents Worksheet - As basic as it gets.
- Difficult Worksheet - I would only have students that have mastered the basic skills start to work with these problems.

- Answer Keys - These are for all the unlocked materials above.

### Algebra Based Quotient Rule Worksheets

It's a lot of combine like factors and solve.

- Practice 1 - There are mixed binominals. The same basic strategy applies, but now you have two variables to contain.
- Practice 2 - Don't forget about the whole numbers. We use larger constants here.
- Practice 3 - Solve for the following. Do not disregard the constant values before you finish.
- Practice 4 - Simplify for the following. Students find it more difficult to work with problems that lack base numbers.

### Multiple Variable Quotients of Exponents Worksheets

Simplify these as far as you can.

- Practice 1 - Simplify the following exponent problems. Remember that all of the answers will contain positive exponents.
- Practice 2 - Everything is positive. Just trust me on that.
- Practice 3 - Know when to subtract and add. There will be some negative values, but it will all work out in the end.
- Practice 4 - Write your answers using positive exponents only.

### Positive and Negative Quotients of Exponents Sheets

Simplify these guys. Remember that all of your answers will be positive.

- Sheet 1 - A nice mix for reviews. You might want to review how negative and positive integers interact.
- Sheet 2 - Some movement here is great. Remember that minus a minus is a plus.
- Sheet 3 - Solve for the following division of exponents.

### Additional Division Based Problems Sheets

Practice makes perfect!

- Sheet 2 - You can't get much too closer than solving these.
- Sheet 3 - This worksheet covers a lot of ground.
- Sheet 4 - Another one that gets easier as it goes along.
- Sheet 5 - Remind yourself how to line up the dividend and divisor.
- Sheet 6 - This should be a quick one for your students.

### Difficult Problems

Again, these are for students that have a good handle on what they are doing.

- Practice 2 - These really step up the level of critical thinking.
- Practice 3 - We would suggest planning how you will perform these calculations before you attempt them.

### Tips for Dividing Exponents

Exponents are a quick way to display very large or small values using the base ten number system. The value 100,000 can be written as 10^{4}. The 4 represents the number of zeroes found after 10.

The lesson will be going over a key rule in the world of exponents which is related to the quotient rule. This rule can be used for dividing exponents. When exponents have the same base and we are trying to find their difference, we simply need to find the difference between the exponents. It follows the flow: (a^{b} / a ^{c}) = a^{b - c}. Let's try understanding this with a few examples.

Suppose that you have the responsibility of handing out the jellybeans at a party. You have around 1,000,000,000 jellybeans to divide evenly among 10,000 people. You already know that you need to divide the numbers. But there is an easier way of doing it rather than using the long division method. We can use exponents.

1,000,000,000 has 9 zeros which can be written as 10^{9} and 10,000 can be written as 10^{4}. What we need to do here is divided 10^{9} with 10^{5}. It will help us determine how many jellybeans with be divided among the members.

The exponent rule of quotient dictates that we can subtract the exponent below from the upper exponent considering the base is the same.

10^{9} - 10^{4} = 10^{5}. Our final answer is 10^{5} which means that every person will get 100,000 jellybeans. That is a lot of jellybeans for a single individual.