Chapter 2: Power and Exponent Laws
What You'll Learn...
• Use powers to show repeated multiplication
• Evaluate powers with exponent 0
• Write numbers using powers of 10
• Use the order of operations with exponents
• Use the exponent laws to simplify and evaluate expression
Key Words
integer
opposite
positive
negative
factor
power
base
exponent
squared
cubed
standard form
product
quotient
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Investigation ­ Page 52
Use the square tiles below, create as many different­sized larger squares as you can.
Write the area as a product. Record your results in a table.
Number of Tiles
1
Area (Square Units)
1
Side Length (Units)
1
Area as a Product
1 x 1 What pattern do you see in the table? Use the patterns to predict the areas of the next three squares.
2
Use the cubes to make as many different­sized larger cubes as you can. Write the volume of each cube as a product. Record your results in a table.
Number of Cubes
1
Volume
(Cubic Units)
1
Edge Length (Units)
1
Volume as a Product
1 x 1 What pattern do you see in the table? Use the patterns to predict the volumes of the next three cubes.
3
Connection
When an integer, other than 0, can be written as a product of
equal factors, we can write the integer as a power.
2 x 2 x 2 x 2 x 2 is 25.
2 is the base.
5 is the exponent.
25 is the power.
25 is a power of 2.
5
2
base
exponent
25
power
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Connection
• A power with an integer base and exponent 2 is a
square number.
3 ways to write 25
Standard form: 25
As repeated multiplication: 5 5
As a power: 52
We say: "5 squared or 5 to the 2"
• A power with an integer base and exponent 3 is a
cube number.
3 ways to write 125
Standard form: 125
As repeated multiplication: 5 x 5 x 5
As a power: 53
We say: "5 cubed or 5 to the 3"
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Review of Integer Rules...
(+)(+) = (+)
(­)(­) = (+)
same sign ­ positive answer
(+)(­) = (­)
(­)(+) = (­)
different signs ­ negative answer
When multiplying 2 integers
if integers have the same sign
the product is positive
ie: 3 x 5 = 15
(­3) x (­4) = 12
if integers have different signs the product is negative
ie:
(­4) x 5 = (­20)
6 x (­2) = (­12)
When multiplying more than 2 integers
when the number of negative integers is even
the product is positive
ie:
=
=
(­3)(­2)(4) (6)(4)
24
when the number of negative integers is odd,
the product is negative
ie:
=
=
(­3)(­2)(­4)
(6)(­4)
(­24)
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Ex:
Write as a power.
a)
b) 7
4 x 4 x 4 x 4 x 4 x 4
c)
2 x 2 x 2 x 2
e)
(­7)(­7)(­7)(­7)(­7) d) (­9)(­9)(­9)
Example: Write as repeated multiplication and in standard form.
a) 35 b) 74
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Powers with brackets...and negative signs...
(­3)2 means (­3 x ­3) = 9
­32
means
­(3 x 3) = ­9
­(­3)2
means
­(­3 x ­3) = ­9
­(­32)
means
(­)(­)(3 x 3) = 9
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