1 Exponents I. Vocabulary: A. Label the following using base, exponent,and power. B. Write in expanded form. 3 5
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Exponents
I. Vocabulary:A. Label the following using base, exponent,and power.
B. Write in expanded form.
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II. Reading and Writing PowersExponential Words Meaning
Form
A.
B.
C.
D.
E.
F.
101
four squared
5 5 5
negative seven to the sixth power
x n
the opposite of the quantity seven to the fourth power
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Ex:1 Write the expression using an exponent.
a) 6 6 6 b) 4 y x y
c) (3)(3)(3)(3)
Ex: 2 A microscope can magnify a specimen 103 times. How many times is that?
Ex: 3 Simplifya) 62 b) Evaluate a4 and (a)4
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III. Order of Operations/Evaluating Powers
Ex 1. Simplify 3(1 + 4)3
Ex 2. Evaluate 7(w + 3)3 + z when w = 5 and z = 6.
You Try:3) 2 52 + 4 (3)3 4) Evaluate 3a2 + 6, for a = 5
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Ch [4.7] Multiplication Laws of Exponents
ex 1:
Law 1: Multiplying Same Bases-
Expand:
How many x's do we have?
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Law 1: Multiplying Same Bases-
"Product of Powers" - ADD Exponents
ex a)
ex b)
ex c)
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Law 2: Power of a Power-Raising one Power to another one!
Ex 2:
Expand:
How many x's do we have?
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Law 2: Power of a Power-"Power of a Power" - Multiply exponents together when raising one to another.
ex a)
ex b)
ex c) VS.
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[4.8] Zero, Division, and Negtive Laws of Exponents
ex a:
Law 3: Zero Exponent
Any base to the zero power is 1, except the base ______.
ex b:
ex c: 7
ex d:
ex e:
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Complete the following chart.
1.
2.
3.
Power Expanded Form Cancel Simplified Expanded Form
Exponential Form
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Law 4: Dividing Powers
Quotient of Powers Property:To divide powers with the same base, ___________ the exponents.
[4.8] Division Properties of Exponents
Examples:1. 2. 3.
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Any base raised to a negative exponent...____________________________.
Law 5: Negative Exponents
(is reciprocated: flipped over!)
Let's look at what we know first...
negative exponents do NOT make your base negative!
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You Try: Simplify each expression
1. 2.
Write each expression without a fraction bar.3. 4.
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Law 1: Law 2: Law 3:
Organize today's material in your own words!
Law 4: Law 5:
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Homework:Worksheet
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Worksheet Answers:1. 2. 5 3. 2m3n 4. 2a6b2
5. 9x14y13 6. 7. 3c2 8. d
9. 10. 11. 12.
13. 14. 15. 16.
17. 36a7b7 18. 5x4 19. 20. 5m3t6
21. 22. 23. 24. 75r9t20