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Transcript
Unit 2 – Powers and Exponent Laws
2.1: What is a Power?
Math 9
Investigate (page 52):
Squared:
Use the tiles to make as many different-sized larger squares as you can. Write the area of each square as
a product. Record your results in a table.
Number of Tiles
Area (square units) Side Length (units) Area as a Product
1
1
1
1X1
4
4
2
2X2
9
9
3
3X3
16
16
4
4X4
25
25
5
5X5
36
36
6
6X6
49
49
7
7X7
64
64
8
8X8
Hints:
-
Area = side length X side length (1unit X 1 unit = 1 square unit)
How many tiles would you need to show a square with a side length of 2? (4)
Could you use tiles to show an area of 2? (yes, but it would be a rectangle)
The side length of the squares increases by 1 each time.
Patterns:
o In each row, the number of tiles is equal to the area of the square. The area is the product of 2 side lengths.
Cubed:
Use the cubes to make as many different-sized larger cubes as you can. Write the volume of each cube as
a product. Record your results in a table.
Number of Cubes
Volume (cubic
Edge Length
Volume as a
units)
(units)
Product
1
1
1
1X1X1
8
8
2
2X2X2
27
27
3
3X3X3
64
64
4
4X4X4
125
125
5
5X5X5
216
216
6
6X6X6
Hints:
-
Volume = length X width X height (3 X 3 X 3 = 27)
Check answer by taking cube apart and counting all the cubes.
How do you know that you have made a cube? (Its length, width and height are the same).
The edge length of the cubes increases by 1 each time.
Patterns:
o In each row, the number of cubes is equal to the volume of the cube. The volume is the product of 3 edge
lengths.
Reflect & Share:
Area is a measure of the amount of surface area.
Ex. Square = 5 X 5 = 25 = 52
Volume is a measure of the amount of space occupied.
Ex. Cube = 5 X 5 X 5 = 125 = 53
Unit 2 – Powers and Exponent Laws
Math 9
Connect:
Introduce base, exponent and power to students, and go through example. Give students some numbers
and have them write them in Standard Form, Repeated Multiplication and as Powers.
9 squared = 81 (standard)
= 9 X 9 (repeated multiplication)
= 92 (as a power)
Example 1 – Writing Powers
Write as a power.
a) 7 X 7 X 7 X7 = 74
9 cubed = 729 (standard)
= 9 X 9 X 9 (repeated multiplication)
= 93 (as a power)
b) 2 X 2 X 2 X 2 X 2 X 2 X 2
X 2 = 28
Example 2 – Evaluating Powers
Write as repeated multiplication and in standard form.
a) 26 = 2x2x2x2x2x2
b) 64 = 6x6x6x6
= 64
= 1296
c) 6 = 61
c) 55 = 5x5x5x5x5
= 3125
Assignment: pg 55-56
#4, 5, 7 (a,b,c), 8 (a,b,c), 9(a,b,c), 11, 12(a,b,c,d)
Quick Review:
1. Identify the base, exponent.
a) 78
Base= 7
Exponent=8
b) 23
Base= 2
Exponent=3
2. Write the following as a power and in standard form
a) 4x4x4 = 43
= 64
b) 6x6 = 62
=36
Example 3 – Evaluation Expressions Involving Negative Signs
- When the negative sign is within the brackets, the base is a negative integer. When the
negative sign is outside the brackets, it changes the value of the power.
Identify the base of each power, then evaluate the power.
a) (-2)3 = (-2)(-2)(-2)
Base = -2
= -8
c) - (-4)3 = - (-4)(-4)(-4)
= - (-64)
b) -54 = -(5x5x5x5)
Base = 5
= 64
= -625
Base = -4