1. NOTES ON EXPONENTS When working with numbers, exponents are used to tell us how many times a factor is repeated in a multiplication problem. For example, rather than having to write 2x2x2x2x2 you could simply write 2 5 which means the same thing. You read this by saying 2 to the fifth power. Change the following longer strings of factors to shorter strings using exponents: 3x3x3x3x3x3_______ 4 x 4 x 4 _______ 7x7x7_______ 10x10x10x10_______ 5959 base Exponent

2. When solving a problem where you have an exponent, you need to list out the string of factors, then multiply carefully making sure to cross out numbers when they've been used. Example: 2 3 = 2 x 2 x 2 5 4 = 5 x 5 x 5 x 5 10 6 = 10 x 10 x 10 x 10 x 10 x 10

3. SPECIAL RULES FOR EXPONENTS: We sometimes say that something to the second power is "squared". Something to the third power is "cubed". SHORTCUT for 10: Write the number 1, and add as many zeros as the exponent. Example: 10 8 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000 10 6 = 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 10 5 = 10 3 =

4. ORDER OF OPERATIONS Order of operations helps us to know what to do first when you have multiple operations in one problem. Example problem: 2 x 3 + 5 - 10 = ___ You have likely learned this in the past as PEMDAS or "Please Excuse My Dear Aunt Sally" P = E = M = D = A = S = A common mistake is to think that that multiplication comes before division and addition comes before subtraction - THIS IS NOT TRUE!!!

5. Parentheses Exponents Multiplication and Division in order from L to R Addition and Subtraction in order from L to R Try to view order of operations as a pyramid and that you will alwasy work from the top of the pyramid toward the bottom. Think to yourself, "what level of the pyramid am I on now?" You may need mulptiple rows of work to solve one problem!! Example problem: 9 2 + (3 x 5) = _____

6. What's the difference in how you'd solve these problems? Notice they have the same numbers, but a different answer!! 12 3 x 2 = 12 (3 x 2) =

7. Solve the following problems using the correct order of operations: 4 + 6 x 3 3 = _____ (12 - 9) x (6 + 1) = _____ 6 3 + 4 x 5 = _____

9. Using addition, subtraction, multiplication, and division, put the correct signs in the correct places to make the problem work correctly!