Working with exponents
| Lessons | These lessons explain exponent notation, the advantage of using exponent notation, and the rules involved when doing so. |
|---|---|
| Lesson 1 | Explains what exponent notation is and its benefits. Develops the multiplication rulefor exponent notation. |
| Lesson 2 | Develops the division rule for exponent notation. |
| Lesson 3 | Uses the division rule shown in lesson 2 to give meaning to exponents that are … a) Zero. b) One. c) Negative integers. |
| Lesson 4 | When a term that already has an exponent is raised to a power, a simple rule can be used. This lesson develops that rule. |
| Lesson 5 | Uses the “power of power” rule shown in lesson 4 to show how fractional powers can be understood in terms of roots. This completes the meanings for all kinds of exponents, including the “non-standard” exponents that cannot be described in terms of “lots of the same value multiplied together”. a) Zero. b) Positive integers, including 1. c) Negative integers including negative 1. c) Positive fractions. d) Negative fractions. |
| Lesson 6 Lesson 7 (to be done) | For curious mathematics students. The exponent rules were developed based on the definition of exponents with integer powers greater than or equal to 2. Strictly speaking, those rules cannot be assumed to be true for other powers. Lesson 6 proves the rules are also true for NEGATIVE INTEGERS. Lesson 7 proves the rules are also true for POSITIVE FRACTIONS. Click herefor a more comprehensive set of proofs. |
| Lesson 8 (to be done) | Shows how multiplication, division and powers of powers can be used in various combinations. |
| Lesson 9 (to be done) | Shows how to solve equationsthat contain exponential terms. |