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## Properties of Exponents and Roots

#### 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  #### 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.

• Quiz 1 - We can combine the values into one exponent.
• Quiz 2 - Find the value of expression.
• Quiz 3 - Where does it end?