1. Bell Work 12/10

2. Objectives The student will be able to: 1. multiply monomials. 2. simplify expressions with monomials.

3. A monomial is a 1.number, 2.variable, or 3.a product of one or more numbers and variables. Examples: 5 y 3x 2 y 3

4. Why are the following not monomials? x + y addition division 2 - 3a subtraction

5. Multiplying Monomials When multiplying monomials, you ADD the exponents. 1) x 2 x 4 x 2+4 x6x6 2) 2a 2 y 3 3a 3 y 4 6a 5 y 7

6. Simplify m 3 (m 4 )(m) 1.m 7 2.m 8 3.m 12 4.m 13

7. Power of a Power When you have an exponent with an exponent, you multiply those exponents. 1) (x 2 ) 3 x 2 3 x6x6 2) (y 3 ) 4 y 12

8. Simplify (p 2 ) 4 1.p 2 2.p 4 3.p 8 4.p 16

9. Power of a Product When you have a power outside of the parentheses, everything in the parentheses is raised to that power. 1) (2a) 3 23a323a3 8a 3 2) (3x) 2 9x 2

10. Simplify (4r) 3 1.12r 3 2.12r 4 3.64r 3 4.64r 4

11. Power of a Monomial This is a combination of all of the other rules. 1) (x 3 y 2 ) 4 x 3 4 y 2 4 x 12 y 8 2) (4x 4 y 3 ) 3 64x 12 y 9

12. Simplify (3a 2 b 3 ) 4 1.12a 8 b 12 2.81a 6 b 7 3.81a 16 b 81 4.81a 8 b 12

13. Bell Work 12/12 Simplify

14. Objectives The student will be able to: 1. divide monomials. 2. simplify negative exponents.

15. When dividing monomials, subtract the exponents. 1. 2. Dividing Monomials = m 6 n 3 = b 5-2 = b 3 = m 7-1 n 5-2

16. = xy = 9a 3 b 2

17. Simplify 1.48g 2 h 2 2.48gh 2 3.4g 2 h 2 4.4gh 2

18. = 1m 0 n Here’s a tricky one! What happened to the m? = n They canceled out! There are no m’s left over! This leads us to our next rule…

19. Zero Exponents Anything to the 0 power is equal to 1. a 0 = 1 True or False? Anything divided by itself equals one. True! See for yourself!

20. A negative exponent means you move the base to the other side of the fraction and make the exponent positive. Negative Exponents Notice that the base with the negative exponent moved and became positive!

21. Simplify. 6.x -4 y 0 You can not have negative or zero exponents in your answer.

22. 1.p 2 2.p 12 3.. 4.. Simplify

23. Simplify. You can’t leave the negative exponent! There is another way of doing this without negative exponents. If you don’t want to see it, skip the next slide!!!

24. Simplify (alternate version). Look and see (visualize) where you have the larger exponent and leave the variable in that location. Subtract the smaller exponent from the larger one. In this problem, r is larger in the numerator and s is larger in the denominator. Notice that you did not have to work with negative exponents! This method is quicker!

25. Simplify. Get rid of the negative exponent.

26. Get rid of the negative exponents. Simplify.

27. Get rid of the parentheses. Simplify. Get rid of the negative exponents.

28. 1.. 2.. 3.. 4.. Simplify

30. Objective The student will be able to: express numbers in scientific and decimal notation.

31. How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

32. Scientific Notation A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 10 and n is an integer

33. Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

34. 2. 10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 10 23

35. 1) Express 0.0000000902 in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10 -8

36. Write 28750.9 in scientific notation. 1.2.87509 x 10 -5 2.2.87509 x 10 -4 3.2.87509 x 10 4 4.2.87509 x 10 5

37. 2) Express 1.8 x 10 -4 in decimal notation. 0.00018 3) Express 4.58 x 10 6 in decimal notation. 4,580,000

38. Write (2.8 x 10 3 )(5.1 x 10 -7 ) in scientific notation. 1.14.28 x 10 -4 2.1.428 x 10 -3 3.14.28 x 10 10 4.1.428 x 10 11

39. Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 4) 234.6 x 10 9 2.346 x 10 11 5) 0.0642 x 10 4 6.42 x 10 2

40. Write 531.42 x 10 5 in scientific notation. 1..53142 x 10 2 2.5.3142 x 10 3 3.53.142 x 10 4 4.531.42 x 10 5 5.53.142 x 10 6 6.5.3142 x 10 7 7..53142 x 10 8