### R.4 Exponents

1: Introduction to Exponents

This video covers:

*What is an exponent and how it simplifies

*Review of R.1 Video #4: Introduction to Exponents and Roots

Vocabulary: Base, Power, Exponent, Integer,

Examples:

2: Exponent Properties 1, 2, 3 - Multiplication, Division, Zero Power

This video covers:

*The Exponent Properties included here:

*Proofs of why each of the properties above work

*How the exponent properties build on each other

Examples:

3: Exponent Property 4 - Negative Exponents (Bad Attitude)

This video covers:

*The Exponent Property included here:

*Proof of why the property above simplifies

*What is meant when the words "bad attitude" are mentioned

*How you can simplify each expression in multiply ways

Examples:

4: Exponent Properties 5, 6 - Powers on the Outside of the Parenthesis

This video covers:

*The Exponent Properties included here:

*Proofs of why each of the properties above work

*Why you need to distribute powers to all bases, including the numbers and not just the variables

Examples:

5: Exponent Properties 7, 8 - Fractions with Powers, Including Negative Powers

This video covers:

*The Exponent Properties included here:

*Proofs of why each of the properties above work

*Why you need to distribute powers to all bases, including the numbers and not just the variables

*Why you should simplify the inner most part of the expression before distributing outside exponents

*Why you cannot distribute powers when the inside operation is addition or subtraction

Examples:

6: Exponent Examples - Combining All Properties in Examples

This video includes:

*A recap of all the 8 exponent properties

*The best route to simplify exponent properties when there are multiple operations

*The difference between a negative exponent and a negative base

*What checks to do to make sure you are finished

*Why I don't give exact homework problems as examples

Examples:

7: Introduction to Scientific Notation

This video covers:

*What scientific notation is, including the proper format, and why it is important

*Definition of notation

*A real life example of scientific notation

*Converting from scientific notation to standard decimal notation

*Converting from standard decimal notation to scientific notation

Examples:

8: Multiplying and Dividing Scientific Notation Numbers

This video covers:

*The easiest way to multiply and divide numbers in scientific notation

*Review of how to simplify exponents when multiplying or dividing the same bases

*Reminder to write answers in scientific notation and how to adjust by one unit if necessary

Examples: