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8 th Grade Math: Exponents

8 th Grade Math: Exponents. 4.2 Negative and Zero Exponents 4.3 Rules for Exponents. Exponents and Rules. Be able to multiply and divide monomial expressions with integer exponents . Review:. Exponent -how many bases you multiply. 3 2. Base (Big Number) -the number you multiply.

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8 th Grade Math: Exponents

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  1. 8th Grade Math: Exponents 4.2 Negative and Zero Exponents 4.3 Rules for Exponents

  2. Exponents and Rules Be able to multiply and divide monomial expressions with integer exponents.

  3. Review: Exponent -how many bases you multiply 32 Base (Big Number) -the number you multiply Exponent – repeated multiplication 32 means 3●3

  4. 4.2 Exploration

  5. Why? Does this work? Let’s Follow a Pattern ? = = 81 –1 ÷3 = 27 –1 = 1 ÷3 = 9 –1 ÷3 = 3 –1 ÷3 1 1 =

  6. Let’s Extend the Pattern = 9 A negative exponent means to divide by that number of factors instead of multiplying. –1 ÷3 = 3 –1 ÷3 = 1 –1 ÷3 = 1/3 –1 ÷3 = 1/9

  7. n x x x x x x n n 1 1 x x 1 1 – – = = = x x -n x x x x n n x x Negative Exponents “Cross the line change the sign” • Negative exponent is in the numerator, then move the variable/number to the bottom and change the negative exponent to positive exponent. • Negative exponent is in the denominator, then move the variable/number to the top and change the negative exponent to positive exponent.

  8. The six is not included with the negative exponent! Examples: Write using only positive exponents. 1. a-3 = 3. 6y-7 = 4. (6y)-7 =

  9. Examples: Write using only positive exponents.

  10. Assignment • Pg. 168-169 #13-20, 24, 57 • In your own words write the Objective of today’s lesson and rate your understanding using our Scale.

  11. 4 n Warm-up 1-10-14 Write in exponential form. 1. n•n•n•n 2. (–8) • (–8) • (–8) • (h) (–8)3h 256 3.Evaluate (–4)4 4. Evaluate x • z – yx for x = 5, y = 3, and z = 6. –213 Talk with your group about yesterday’s assignment.

  12. Examples: Write using negative exponents. (No Fractions!) X-6 4b-4

  13. Tear it Up! • Directions: • Take your sheet of paper. Fold it in half. How many layers or folds are there? • Repeat process until you cannot fold it any more. • Predict how many layers there would be once you can no longer fold your paper. You may use your calculator. • Now open your sheet up. Tear it down the middle. How much of the original sheet do you have? • Tear your sheet in half again. How much of the original sheet do you have? • Repeat process and complete table.

  14. Solution!

  15. Solution!

  16. Summary: • What is the relationship between the number of folds and the number of layers? • What happens to the paper as the number of tears increases?

  17. Video

  18. Practice • Grab your white board, and let’s practice simplifying expressions with exponents.

  19. Warm Up 1-13-14 You have 10 minutes to begin working on Countdown Week 14. Take out your notes packet from last week.

  20. 4.3 Exploring Exponent Properties • Step 1: Write each product below in expanded form and then rewrite it in exponential form with a single base.

  21. Step 2: Compare the exponents in each final expression to the exponents in the original product. Describe a way to find the exponents in the final expression without using expanded form. • Step 3: Generalize your observations:

  22. Product Rule When multiplying powers with the same base, the exponents are added. In general: am● an = am+n SAME BASE!

  23. Examples: 1. 2. 3. 4.

  24. Rewrite each quotient in expanded form and then in exponential form.

  25. Quotient Rule When dividing powers of the same base, exponents are subtracted. In general: am÷ an = am-n SAME BASE!

  26. DO NOT divide the bases! Examples: Example 1: 56 ÷ 52= 56-2 =54 1. 2. 3.

  27. Big Ideas • Turn to a partner and tell him or her what the Product Rule means. • Have your partner explain the Quotient Rule to you.

  28. Today’s Assignment • Write the objective of today’s lesson on your assignment and rate yourself with our scale. • Complete p. 172 – 173 (#1 – 8, 41, 43, 49, 57)

  29. Warm Up 1-14-14 Evaluate. 1. 3-3 2. m-2· m0· m2 when m = 9 1 16 3.b2 for b = 4 18 4. n2r for n = 3 and r = 2 Take out yesterday’s assignment.

  30. 4.3 Power Rule Rewrite each in expanded form and then write in exponential form.

  31. 4.3 Power Rule When you have a power to a power, you multiply the exponents. In general: (am)n = am●n

  32. Let’s try these together: Rewrite (x3)4 with a single exponent. • (x3)4 = x3 ● x3 ● x3 ● x3 = Here is a product raised to a power. Begin by expanding: • (xy)3 = xy ● xy ●xy = x ● x ● x ● y ● y ● y =

  33. Examples: a. (a5)3 c. [(x2)2]2 b. (42)3 d. (ab)4

  34. More Examples e.(5x)3  g. (a2b3)4 f. (4xy)5 h. (43x7y4)5

  35. Summary • In the left column of your note sheet, write a sentence to summarize the Power Rule.

  36. Today’s Assignment Add these problems to yesterday’s assignment: p. 172 – 173 (#9 – 12, 42, 44, 45) Rate your understanding of the power rule with our scale.

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