Ch 15: MTEL Middle School Mathematics: Roots & Powers

About This Chapter

This chapter on roots and powers is the perfect way to prepare for the related portions of the MTEL Middle School Mathematics exam, with easy-to-follow video lessons giving you a significant confidence boost going into the test.

MTEL Middle School Mathematics: Roots and Powers - Chapter Summary

This chapter covers a variety of mathematical operations and principles related to roots and powers, providing a thorough yet time-efficient review of the topics you'll want to have down going into the exam. By the end of this chapter, you'll be ready to tackle questions concerning all of the following:

  • Radical expressions and radicands
  • Roots and powers of algebraic expressions
  • Simplifying square roots of quotients
  • Exponents and exponential notation
  • Product and quotient of powers
  • Zero and negative exponent
  • Fractional powers
  • Estimating square roots and simplifying radical expressions that contain square roots
  • Simplifying square roots of powers in radical expressions
  • Calculating with surds

Depending on your learning preference, you can choose to review the lesson through a video or transcript of the content. When you're done, you'll be able to check your understanding of the lesson material with a practice quiz that you can take and re-take until you feel comfortable.

14 Lessons in Chapter 15: MTEL Middle School Mathematics: Roots & Powers
Test your knowledge with a 30-question chapter practice test
Radicands and Radical Expressions

1. Radicands and Radical Expressions

It's easy to see that funky radical symbol and panic just a little bit. There are so many rules that go along with it, it's hard to keep up with them all. This lesson will help by describing what you should do when you are faced with a square root.

Roots and Powers of Algebraic Expressions

2. Roots and Powers of Algebraic Expressions

In this lesson, you'll learn about some common mistakes that students make when working with roots and powers of algebraic expressions on the SAT and how to make sure you don't fall into the same trap.

Simplify Square Roots of Quotients

3. Simplify Square Roots of Quotients

The quotient rule can be used to simplify square roots of quotients. This lesson will define the quotient rule and show you how it is used to simplify square roots.

What Are Exponents? - Definition, Properties & Rules

4. What Are Exponents? - Definition, Properties & Rules

Exponents are the mathematical shorthand that tells us to multiply the same number by itself for a specified number of times. This lesson will not only explain how the exponent works but also discuss the seven distinct properties, or rules, that govern its use.

How to Use Exponential Notation

5. How to Use Exponential Notation

Exponential notation is a mathematical method for writing longer multiplication problems in a simplified manner. This lesson will define how to work with exponential notation and give some examples of how it is used.

Product Of Powers: Definition, Rule & Property

6. Product Of Powers: Definition, Rule & Property

The product of powers rule states that when multiplying two powers with the same base, just add the exponents. Confused yet? This lesson will clear everything up, give some examples and provide a quiz for you to test your knowledge.

Quotient Of Powers: Property & Examples

7. Quotient Of Powers: Property & Examples

The quotient of powers rule states that when dividing two powers with the same base, just subtract the exponents. Don't worry if that doesn't make sense off the bat; this lesson will clear everything up, give some examples, and provide a quiz for you to test your knowledge.

Zero Exponent: Rule, Definition & Examples

8. Zero Exponent: Rule, Definition & Examples

The zero exponent rule states that any term with an exponent of zero is equal to one. This lesson will go into the rule in more detail, explaining how it works and giving some examples. There will also be a quiz to test your knowledge.

Negative Exponent: Definition & Rules

9. Negative Exponent: Definition & Rules

Negative exponents have caused problems for math students as long as they have been defined. This lesson will shed some light on the negative exponent: what it means and how to work with it in a math problem.

Working With Fractional Powers

10. Working With Fractional Powers

If you know what to do with 3 to the second power, then you understand exponents. But what if the exponent is a fraction? Find out what to do with fractional powers in this lesson.

Estimating Square Roots

11. Estimating Square Roots

Inverse operations are mathematical operations that undo each other. The square root is the inverse of the squared (or multiplying a number by itself) operation. There is an easy method for estimating the square root of a number, which you will learn in this lesson.

Simplifying Expressions Containing Square Roots

12. Simplifying Expressions Containing Square Roots

In order to write radical expressions correctly, they have to be written in their simplest form. This lesson will show you how to simplify expressions containing numbers and variables inside a square root.

Simplifying Square Roots of Powers in Radical Expressions

13. Simplifying Square Roots of Powers in Radical Expressions

Simplifying radical expressions that contain powers can be tricky. There are a few simple rules that will help you perform these simplifications with ease. This lesson will teach you how.

How to Calculate with Surds

14. How to Calculate with Surds

Finding distances and lengths often involves a type of square root called a surd. In this lesson, we show some interesting examples of calculating with surds.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

Other chapters within the MTEL Mathematics (Middle School)(47): Practice & Study Guide course

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