## Rewriting Radical and Exponential Expressions

#### Aligned To Common Core Standard:

**High School** - HSN-RN.A.2

How to Rewrite Radical and Exponential Expressions - Solving questions in a radical form can be difficult; thus, it can be easier to rewrite the equation in rational exponents. You can write an equation to exponential form by using these steps. Let us give an example where you have to solve ^{3} √8^{2} .
Now, by the first look, it can be difficult to solve. To convert it into exponential expressions, you can rewrite them as: ^{3} √8^{2} = 8^{2/3}. Now, you can further break down the expression as follows: 8^{2/3} = (8^{1/3})^{2}. Now, it’s in exponential form, which is easier to solve. The cube root of 8 is two, and by squaring it, the result becomes 4.
A series of worksheets and lessons that will show you how to rewrite both radical and exponential expressions.

### Printable Worksheets And Lessons

- Radical Expressions
Step-by-step Lesson- Start working on simplifying radical expressions.

- Guided Lesson
- We include radical products in this batch just to uncomplicate
things.

- Guided Lesson Explanation
- These problems can take up quite a bit of room to work out.

- Practice Worksheet
- Radical products, radical quotients, and basic radicals. What's
with the shark?

- Matching Worksheet - Definitely give the kids some scrap paper to work with on this one.
- Simplify Radicals Five Pack- Take the radical and make it simple to work with.
- Solving Exponential Equations (lacking a common base) Five Pack - The title pretty much says it all.
- Exponential Expressions and Equations Worksheet Five Pack - You are solving for x. They are mostly fractional exponents.
- Rationalize Denominators Worksheet Five Pack - You are also looking for conjugates of binomials and determining equivalent expressions.
- Evaluating Rational (Fractional) Exponent Worksheet Five Pack - I had to do a little refresher for myself before writing this one.

#### Homework Sheets

Use the properties of multiplication and roots to help you simplify the problems.

- Homework 1 - We need to break the square into smaller parts to simplify it.
- Homework 2 - To finish simplifying the expression, multiply by the whole to rationalize the denominator.
- Homework 3 - You can use the multiplication property of square roots.

#### Practice Worksheets

We removed clipart from the second and third versions to save you some ink.

- Practice 1 - Simplify the following expressions.
- Practice 2 - The multiplication property of square roots tells us that: √ab = √a × √b
- Practice 3 - A nice strategy is to group perfect square factors.

#### Math Skill Quizzes

Remind your students that the letter used as the unknown variable is negligible. We get a few question about that from time to time.