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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