NOTES ON EXPONENTSWhen 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 25 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 _______

59base

Exponent

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:

23 = 2 x 2 x 2

54 = 5 x 5 x 5 x 5

106 = 10 x 10 x 10 x 10 x 10 x 10

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: 108 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000

106 = 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000

105 = 103 =

ORDER OF OPERATIONSOrder 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!!!

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: 92 + (3 x 5) = _____

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) =

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 = _____

Using addition, subtraction, multiplication, and division, put the correct signs in the correct places to

make the problem work correctly!

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