1. 2.1 Simplifying Expressions
Term: product or quotient of numbers, variables, and variables raised to powers
Coefficient: number before the variables If none is present, the coefficient is 1
Factors vs. terms: In “5x +y”, 5x is a term. In “5xy”, 5x is a factor.

2. 2.1 Simplifying Expressions
When you read a sentence, it split up into words. There is a space between each word.
Likewise, an is split up into terms by the +/-/= sign:
The only trick is that if the +/-/= sign is in parenthesis, it doesn’t count:

3. 2.1 Simplifying Expressions
Like Terms: terms with exactly the same variables that have the same exponents
Examples of like terms:
Examples of unlike terms

4. 2.1 Simplifying Expressions
Combining Like Terms: the distributive property allows you to combine like terms
Examples of combining like terms:

5. 2.2 The Product Rule and Power Rules for Exponents
Review: PEMDAS (order of operations) – note that exponentiation is number 2.
Product rule for exponents:
Example:

6. 2.2 The Product Rule and Power Rules for Exponents
Power Rule (a) for exponents:
Power Rule (b) for exponents:
Power Rule (c) for exponents:

7. 2.2 The Product Rule and Power Rules for Exponents
A few tricky ones:

8. 2.2 The Product Rule and Power Rules for Exponents
Examples (true or false):

9. 2.2 The Product Rule and Power Rules for Exponents
Formulas and non-formulas:     

10. 2.3 Integer Exponents Definition of a zero exponent:
Definition of a negative exponent:

11. 2.3 Integer Exponents Changing from negative to positive exponents:
This formula is not specifically in the book but is used often:

12. 2.4 The Quotient Rule
Quotient rule for exponents:

13. 2.4 The Quotient Rule
Examples (true or false):

14. 2.4 The Quotient Rule
Putting it all together (example):

15. 2.4 The Quotient Rule
Another example:

16. 2.5 Scientific Notation A number is in scientific notation if :
It is the product of a number and a 10 raised to a power.
The absolute value of the first number is between 1 and 10
Which of the following are in scientific notation?
2.45 x 102
12,345 x 10-5
0.8 x 10-12
-5.2 x 1012

17. 2.5 Scientific Notation Writing a number in scientific notation:
Move the decimal point to the right of the first non-zero digit.
Count the places you moved the decimal point.
The number of places that you counted in step 2 is the exponent (without the sign)
If your original number (without the sign) was smaller than 1, the exponent is negative. If it was bigger than 1, the exponent is positive

18. 2.5 Scientific Notation Converting to scientific notation (examples):
Converting back – just undo the process:

19. 2.5 Scientific Notation
Multiplication with scientific notation (answers given without exponents):
Division with scientific notation: