1. Exponents An exponent is the number of times the base is multiplied by itself. Example 27 can also be written as 3 This means 3 X 3 X 3

2. Substituting variables for numbers We can also use variables such as X and Y when using exponents. We can define X and Y as integers. For example: 3 = 3 X 3 X 3 = 27 SO: X = (X)(X)(X)

3. Variable A variable is a symbol for a number we don’t know yet like X or Y.

4. Integers Integers include zero, positive and negative numbers. They do not include fractions.

5. Laws of Exponents X = (X)(X)…..(X) (N factors of X) X = 1 (if X = 0) X X = X

6. Practice Write 11 as multiplication. Write u as a fraction using only positive exponents. What is the value of 100 ? Evaluate -5 and (-5)

7. Solutions 1)11 X 11 X 11 = 1331 2)1 u 3)10 4)1 25

8. Multiplying Exponents Same base (X ) (X) = X Be careful I can add the exponents, because X is the base both time. If I had X and Y I could only combine in the exponents were the same.

9. Differences Math is a language (4x) means (4 ) (X ) 4x means 4 (X)(X)(X)

10. Dividing Exponents Step 1: X X = Step 2: X = 1 X Step 3: (X ) (X ) = X

11. Dividing Exponents Step 1: X X = Step 2: (XX) (XXXXXX) (XXXXXX) STEP 3: (XX) (XXXXXX) (XXXXXX) Step 3: (XX) = X

12. x Anything divided by itself is 1. X to the zero power is 1. Example X / X = (X ) (X ) = 1 This works in all cases except for if X is equal to zero.

13. Practice Solve: 1)X X 2) X X = If X = 5 3) X X 4) X X = If X =3

14. Practice Solve: n = 3 729 If x = 64 solve x n = 2

15. Practice Write 12 as multiplication. Write u as a fraction using only positive exponents. What is the value of 125 ? Evaluate -4 and (-4)

16. Distributive Property The Distributive Property of multiplication is the property that states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. The Distributive Property says that if a, b and c are real numbers, then a(b + c) = (a x b) + (a x c)

17. Examples of Distributive property 36 + 8 = 44 Step 1 4 (9 + 2) = Step 2 (4 x 9) + (4 x 2) = Answer 36 + 8 = 44

18. Practice 1)5 (x + 3) 2) x ( y + 9) Are these equal? 3) 25 + 10 = 7 (5 + 0) = 4) 5 + 3 = 20 (3 + 1) =

19. Scientific Notation Definition: A method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10. Example: The Scientific Notation for 10,492 is 1.0492 X 10. Show You Tube Video

20. Practice Convert to Scientific notation 1)7535 2).0027 3).00045 4) 8,456