## Products and Quotients of Exponents and Powers

#### Aligned To Common Core Standard:

**Grade 8 Expressions** - 8.EE.A.1

How Do Exponents Affect Product and Quotient Operations?
Multiplication and division are two basic mathematical operations. There is a simple way of executing these when we are dealing with base numbers. However, their behavior changes a little when applied with exponential numbers. For example, 5 x 3 will give a simple answer of 15, and 15 / 3 will produce 5. But what will happen if we take things up a step? Here is how product and quotient operations work when applied among exponential numbers.
If two exponential terms with the same base numbers are being multiplied with each other, the exponential rule says that the base can be written just once, and their exponents can be added. And, in the case of division, the similar bases can be written once and their exponents subtracted by each other.
Sums like these can be solved using this simple and easy technique, avoiding the application of exponents on each of the base numbers and then multiplying the big numbers that can be time-consuming. Here are two worked examples:
3^{2} x 3^{5}= 3^{2+5} = 3^{7} = 2187

4^{5} / 4^{2} = 4^{5-2} = 4^{3} = 64. This collection of worksheets and lessons shows students how to work with exponent in multiplication and division situations.

### Printable Worksheets And Lessons

- Step-by-Step Lesson- We show students to break each problem into digestible parts first.
- Guided Lesson - Students work on a product based problem and then move into quotients.
- Guided Lesson Explanation - We were able to make them one printable page. Do you feel that it needs more?
- Practice Worksheet 1 - This sheet focuses on products.
- Practice Worksheet 2 - If you start with multiplication, you just know that we are going to move on to division.

#### Finding Products and Quotients with Exponents

Mixed Problems can be found here.

- Sheet 1 - Solve for the following.
- Sheet 2 - Simplify the following problems.
- Sheet 3 - Solve for the following exponent problems.
- Sheet 4 - Simplify the exponents.

#### Product Practice Sheets

More practice for working with multiplication.

- Practice 2 - These problems are compound all over.
- Practice 3 - They can get all the values in a line here.

#### Quotient Based Worksheets

This are necessary for students that just can't quite get it.

- Practice 2 - Powers of Quotients
- Practice 3 - More division in your life.