Exponents Module Overview

Introduction

Have you ever wondered what it means when you're playing around with your calculator and you get a number like 1.489^-08? In this module, we'll explore this mathematical concept of scientific notation which is used to represent very tiny or very large numbers. We'll also take a look at "roots." Square roots and cube roots will be our focus even though these are not the only kinds of roots. In learning these concepts, we'll review the properties of exponents when performing operations that include powers. Learning how to solve equations is a must in mathematics. We will dive into solving equations and even determine the number of solutions that exist for an equation. Did you know there are different kinds of numbers and that every real number can be written as a decimal? In this unit, we'll finish up with defining real numbers and how to estimate irrational numbers based on rational approximations. The fundamental concepts that we will cover in this unit will give you a great start in the exploration of algebraic concepts.

Essential Questions

What are the properties of integer exponents?
How can we take the square root and the cube root of a number?
How can we use square roots and cube roots to solve equations?
What is scientific notation and how can we perform operations with its form?
How do we solve equations in one variable?
How do we know how many solutions exist when we solve an equation?
How do we know if numbers are rational or irrational?
How can we estimate where irrational numbers should be placed on the number line using rational approximations?

Key Terms

The following key terms will help you understand the content in this module.

Additive Inverse - the opposite of a number.

Exponent - The number of times a base is used as a factor of repeated multiplication.

Irrational - A real number whose decimal form is non-terminating and non-repeating that cannot be written as the ratio of two integers.

Radical - A symbol that is used to indicate roots.

Rational - A number that can be written as the ratio of two integers with a nonzero denominator.

Scientific Notation - A representation of real numbers as the product of a number between 1 and 10 and a power of 10, used primarily for very large or very small numbers.

Square Root - One of two equal factors of a nonnegative number.

Cube Root - One of three equal factors of a number.

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