# Power of Products and Quotients Worksheets

This is the type of math you will start to work with as you progress further with algebra. It is often the starting point for you when you are working with complex expressions or expressions. This is a very helpful skill to have mastered when you begin to study precalculus. It also helps you to pivot into many different areas of science. It has a great deal of application within the physical science such as chemistry and physics. This collection of worksheets and lessons shows students how to work with exponents in multiplication and division situations.

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

- 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.

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

### 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.

### 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 through a basic sum calculation. And, in the case of division, the same bases can be written once, and their exponents subtracted by determining the difference. 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

**Explanation:** As we can see both values share a common base (3). We are undergoing multiplication, so this means that we can just find the sum of the exponents. Once we find that sum, the value is restated in standard form.

4^{5} ÷ 4^{2} = 4^{5 - 2} = 4^{3} = 64.

**Explanation:** As we can see both values share a common base (4). We are undergoing division, so this means that we can just find the difference between the exponents. Once we find that difference, the value is restated in standard form.

### Applying This to More Complex Expressions

The Product and Quotient Rule of Exponents apply to all rational exponents, so it can be applied in much more complex expressions in the same way it is applied to simple ones. We just have to return to basics and understand the vocabulary that exists within an exponential expression.

Using the expression: 5x^{3}.

The number 5 serves as a coefficient. You can combine this with other coefficients by simple operations such as addition or subtraction. The base is x and it is raised to a power of 3. It can be operated with other bases named x that are raised to a power of 3 (meaning itself).