Powers and Exponent Laws 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 = L2 A = 52 = 25 V = L3 V = 53 = 125

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

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

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.

Powers of ten and the zero exponent What’s easier to write, 100000000000000000000 or 1020? Number in Words Standard Form Power one million 1 000 000 106 one hundred thousand 100 000 105 ten thousand 10 000 104 one thousand 1 000 103 one hundred 100 102 ten 10 101 one 1

Zero exponent Power Number 44 256 43 64 42 16 41 4 40 1 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.

example 3045 = 3000 + 40 + 5 = (3 x 1000) + (4 x 10) + (5 x 1) 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)

Khan video 2 Khan Video 2

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

2.3 – Order of operations with powers 2.4 – Exponent laws I Chapter 2

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

example 33 + 23 = 27 + 8 = 35 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.

Exponent rules Exponent Laws: am x an = am+n 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

What’s the general rule we can make for exponent division? 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:

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

example Evaluate. a) 62 + 63 x 62 b) (–10)4[(–10)6 ÷ (–10)4] – 107 Remember, BEDMAS, so we do multiplication first before addition. 62 + 63 x 62 = 62 + 63+2 = 62 + 65 = 36 + 7776 = 7812 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

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

2.5 – Exponent laws II Chapter 2

Handout: try to fill in the chart

A power to a power (33)5 = 33 x 33 x 33 x 33 x 33 = 315 Exponent Laws: 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:

Exponent laws (4 x 3)6 = (4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3) What about something like this? Try it! (4 x 3)6 = (4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3) = (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?

Exponent Laws:

example –(24)3 = –24x3 = –212 = –4096 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

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