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Properties of Exponents and Roots

Answer Keys Here

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

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?