Lesson 5: Integral Exponents

Math 10C Module 2 Lesson 5

Module 2: Roots and Powers

Lesson 5 Summary

In Lesson 5 you investigated the following questions:

How are the properties of exponents used to evaluate and simplify algebraic expressions?
How can patterns be used to uncover mathematical truths?

In this lesson you reviewed and applied exponent laws. By examining patterns and using the laws you learned in previous math courses, you were able to discover the zero exponent law and the integral exponent law. You used the quotient law to show that a0 = 1. Through experimentation with licorice, you learned that each time the exponent of a power is reduced by 1, the value of the power is diminished by a factor equal to the base. You used the results of this experiment to uncover the law that eqn150.eps where These laws are summarized in the following chart:

Exponent Law	General Case
Product Law
Quotient Law
Power of a Power
Power of a Product
Power of a Quotient
Zero Exponent Law
Integral Exponent Law

The practice of examining patterns is fundamental to the development of theorems and laws in mathematics. Those laws or rules can then be combined with other patterns to uncover further laws. Thus mathematical truths are revealed.

You learned the exponent information that is summarized in the chart. It is extremely important to understand how the laws work as opposed to just memorizing the shortcuts. There is a lot of information here, and if you find you are forgetting some of the laws, then likely you need to spend more time writing the steps out so you can see what is happening and understand how the laws work.

In the next lesson you will learn about the rational exponent law. You will investigate a pattern that shows how radicals are related to powers and exponents! You will also practise your troubleshooting skills by examining solutions to problems that contain errors.