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Chapter 2

Chapter 2. Powers and Exponent Laws. 2.1 – What is a power? 2.2 – Powers of ten and the Zero exponent. Chapter 2. Khan Academy on Exponents. What is a power?. Squares. Cubes. A = L 2 A = 5 2 = 25. V = L 3 V = 5 3 = 125. powers. Power : The expression of the base and the exponent.

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Chapter 2

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  1. Chapter 2 Powers and Exponent Laws

  2. 2.1 – What is a power?2.2 – Powers of ten and the Zero exponent Chapter 2

  3. Khan Academy on Exponents

  4. What is a power? Squares Cubes A = L2 A = 52 = 25 V = L3 V = 53 = 125

  5. powers Power: The expression of the base and the exponent. 53 Exponent: The number of times that the base will be multiplied by itself. Base: The number that is being repeatedly multiplied by itself.

  6. powers Examples: 53 = 5 x 5 x 5 35 = 3 x 3 x 3 x 3 x 3 What about negatives? How will they work? Are (–3)4 and –34 the same? (–3)4 = (–3) x (–3) x (–3) x (–3) = 81 –34 = –(3 x 3 x 3 x 3) = –81

  7. challenge 1 2 3 4 5 Use these five numbers to make an expression that represents the largest possible number. You can use any operation you like (addition, subtraction, multiplication, division, exponents), but you can only use each number once.

  8. Powers of ten and the zero exponent What’s easier to write, 100000000000000000000 or 1020?

  9. Zero exponent You can try this with other bases, but the result will always be the same. The Zero Exponent Law: Any base to the power of zero will be equal to one.

  10. example Write 3045 using powers of ten. 3045 = 3000 + 40 + 5 = (3 x 1000) + (4 x 10) + (5 x 1) = (3 x 103) + (4 x 101) + (5 x 100)

  11. Khan video 2 Khan Video 2

  12. PG. 55-57 # 4, 5, 7-9 (Ace), 13, 17, 21, 22, 23 PG. 61-62 # 4, 6, 9, 13, 14 Independent Practice

  13. 2.3 – Order of operations with powers2.4 – Exponent laws I Chapter 2

  14. Order of operations What’s the acronym used to remember the order of operations? B E D M A S • Brackets • Exponents • Division • Multiplication • Addition • Subtraction

  15. example Calculate each expression: 33 + 23 (3 + 2)3 33 + 23 = 27 + 8 = 35 Exponents come before Addition in BEDMAS, so we do them first. (3 + 2)3 = 53 = 125 Brackets come before Exponents in BEDMAS, so we do them first.

  16. Exponent rules Try to solve by expanding into repeated multiplication form: 73 x 74 = (7 x 7 x 7) x (7 x 7 x 7 x 7) = 7 x 7 x 7 x 7 x 7 x 7 x 7 = 77 What happens? What kind of rule can we make about the multiplication of powers with like bases? Exponent Laws: am x an = am+n

  17. Exponent rules What about division? Try solving this one to make a general rule: What’s the general rule we can make for exponent division? Exponent Laws:

  18. example Write each expression as a power. a) 65 x 64 b) (–9)10 ÷ (–9)6 b) (–9)10 ÷ (–9)6 = (–9)10-6 = (–9)4 65 x 64= 65+4 = 69 Evaluate: 32 x 34 ÷ 33 32 x 34 ÷ 33 = 32+4-3 = 33 = 27

  19. example Evaluate. a) 62 + 63 x 62 b) (–10)4[(–10)6 ÷ (–10)4] – 107 b) Remember, BEDMAS, so we do inside the brackets, then multiplication, then subtraction. (–10)4[(–10)6 ÷ (–10)4] – 107 = (–10)4[(–10)2] – 107 = (–10)4+2 – 107 = (–10)6 – 107 = 1 000 000 – 10 000 000 = –9 000 000 Remember, BEDMAS, so we do multiplication first before addition. 62 + 63 x 62 = 62 + 63+2 = 62 + 65 = 36 + 7776 = 7812

  20. Pg. 66-68, # 7, 10, 12, 13, 16, 20, 24, 26pg. 76-78, # 4ace, 5ace, 8, 12, 13, 15, 20 Independent Practice

  21. 2.5 – Exponent laws II Chapter 2

  22. Handout: try to fill in the chart

  23. A power to a power From what we’ve learned from the chart, what can we say about the following expression: (33)5 = 33 x 33 x 33 x 33 x 33 = 315 Exponent Laws:

  24. Exponent laws What about something like this? Try it! = (4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3) (4 x 3)6 = (4 x 4 x 4 x 4 x 4 x 4)(3 x 3 x 3 x 3 x 3 x 3) = 46 x 36 What’s the basic rule that we can say about the what happens when we take a product or quotient to a power?

  25. Exponent Laws:

  26. example Evaluate: a) –(24)3 b) (3 x 2)2 c) (78 ÷ 13)3 –(24)3 = –24x3 = –212 = –4096 b) (3 x 2)2 = 32 x 22 = 9 x 4 = 36 c) (78 ÷ 13)3 = (6)3 = 216 Simplify, then evaluate: (6 x 7)2 + (38 ÷ 36)3 (6 x 7)2 + (38 ÷ 36)3 = (42)2 + (32)3 = 422 + 36 = 1764 + 729 = 2493

  27. Pg. 84-86, # 8, 11, 13, 14, 16, 19, 20 Independent Practice

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