## Properties of Exponents and Roots

#### Aligned To Common Core Standard:

**High School** - HSN-RN.A.1

Common Properties of Exponents and Roots
**Properties of exponents** - The properties of exponents are also called operations for these components. Just like the order of the operations, there is a need for you to memorize such operations in order to be successful. There are five properties of exponents:
Product of powers, Power to a power, Power of a product, Quotient of powers, Power of a Quotient, Properties of Roots.
Roots are one of the most common mathematical elements to be used and it is commonly denoted by the symbol √. If the symbol is written alone with another number inside, then it means that it is a square root. If the symbol has a number before it like: 3√ then it means that it is asking for a cube root.
Here are some of the properties of roots:
**Multiplication** - √a x √b = √(ab)
**Addition** - √a + √b ≠ √ (a + b)
**Subtraction** - √a - √b ≠ √ (a - b)
**Division** - √a/√b = √(a/b). These worksheets and lessons will help students understand the basic properties and nature of both exponents and roots.

### Printable Worksheets And Lessons

- Rewriting Exponents Step-by-step Lesson- We work with fractional exponents in this lesson. We show you how roots and squares relate.

- Guided Lesson - A nice relation back and forth with exponents and roots. We also work on a fractional exponents.

- Guided Lesson Explanation - We show you a repeated way for solving problems of this magnitude.

- Practice Worksheet - Find the end value of all the inverse roots and squares we provide you with. They can be quite challenging.

- Matching Worksheet - This will be fun, but difficult at the same time. See how it goes.
- Exponents Five Pack - You are given various expressions. We want you to find the values of those expressions.
- Nature of Roots Sum and Product of Roots Worksheet Five Pack - All addition and multiplication here.

#### Homework Sheets

Practice rewriting exponents in root and vice versa.

- Homework 1 - We currently have the value in exponent form. We want to convert it to a root value. The good thing is that exponents and roots are just the opposite of one another.
- Homework 2 - We have to rewrite in exponent form. If we remember, the root form and exponent form are the inverse of one another.
- Homework 3 - We have to first simplify the given exponent form.

#### Practice Worksheets

I provided brief explanations here to help students along with the skill faster.

- Practice 1 - Rewrite the root in exponential form and calculate the value.
- Practice 2 - The problem we are working on is a bit trickier because the exponent value is a fraction.
- Practice 3 - Calculate the end value of problems.

#### Math Skill Quizzes

Each quiz mixes all the skills that you will find for this level.