## Rational Exponents

#### Aligned To Common Core Standard:

**Grade 6 Expressions** - 6.EE.A.1

We have worked with our core competency as far as exponents so far which states that an exponent is simply a multiple of the root value by how ever many times it is raised to a power. What if that power was fraction? How would you adjust your calculations based on that? When working with a fractional exponent, the denominator of that exponent serves as the degree of radical that it creates. The purpose of the numerator is the power of the term found inside that radical. In order to proficiently use this skill, you should be well versed on the concepts of roots and anatomy of them. Rational exponents lend themself well to many different uses of the quadratic equations. There are also many different financial applications of this type of math that allow us to make reliable forecast and thereby allowing business leaders to make sound decisions. Economists use this technique often to compute interest rates and create various types of financial products. It is often used to understand the concepts of depreciation and inflation. This can help you assess the stunted or diminishing progression of just about anything with a quantitative value. This series of lessons and worksheets will help you better understand the core fundamentals of working with and using rational exponents.

### Printable Worksheets And Lessons

- Simplifying Expressions With Rational Exponents Lesson- In our problem the root value (5) is the same. This tells us that the multiplication property of rational exponents applies.
- Guided Lesson - Reduce the following expressions to their least complex form.
- Guided Lesson Explanation - We will look at work operations within in this seemingly complex expression set.
- Practice Worksheet - Break everything down to the lowest possible form.
- Simplifying Worksheet - You will approach some of the most common forms of operations that are applied to this skill.

#### Homework Sheets

Each of these sheets gets progressively more difficult.

- Homework 1 - You will work with fractional exponents and strive to make sense of them in a simple form.
- Homework 2 - You will advance to the next level and work exponent of fractional bases. It is not as difficult as it first appears.
- Homework 3 - We now add an operation that you must evaluate as well.
- Homework 4 - This can be complicated if do not plan out the steps that you will take along the way.
- Homework 5 - You will need to draw up the steps of your approach for this one too.

#### Practice Worksheets

This selection of sheets will help students better understand the sequence they should use to solve these problems.

- Practice 1 - Write each expression as a radical in simplest form.
- Practice 2 - You may leave improper fractions in the exponent.
- Practice 3 - The focus here is end off with positive exponents.
- Practice 4 - Do not forget that an operation is found within every expression.

#### Quiz Sheets

It is time to see how well you can manipulate this skill.