Exponents are shorthand for multiplication: (5) (5) = 52, (5) (5) (5) = 53. #1
a)
#2
a) (4)(4)(4)
b)
c)
d)
The "exponent" stands for however many times
the term is being multiplied. 5
3
(3 times) 5 x 5 x 5 = 125
The term that's being multiplied is called the "base".
5
3
b) (­6)(­6)(­6)(­6)(­6)
Can you see the difference?
-42
(-4)2
(-1)2=
(-1)3=
(-1)4=
(-1)5=
.
.
.
Did you see a pattern??
(-1)10247=
(-1)29584=
29584
(-1)
10247
(-1)
= -1
Check out pages 55 and 56.
=1
Please complete questions...
I
Love
Math!
Evaluating powers when the base is negative...
If the exponent is even the answer will be positive.
If the exponent is odd the answer will be negative.
Page 55
#9
Page 56
#11
12
13
14
15
16
WARM-UP
1. Write each power as repeated multiplication.
42
(­5)6
2. Write each product as a power, then evaluate.
6 x 6
Write 25 as a power of 5.
­ (­4)(­4)(­4)
3. Predict whether each answer is positive or negative, then evaluate.
41
­63
(­3)5
(­8)5
­(­3)10
4. Evaluate.
­67
Me again... Try these!
Express as a power of 2.
Please complete questions...
Page 56
#20
21 a
22
23
I
Love
Math!
4 = 2
16 = 2
8 = 2
128 = 2
21
10
3
10 5
0
10
10
0
35
For the following chart *choose a number between 1 and 10 as a base of a power
*use your base and the exponent to fill in the power column
*Write the repeated multiplication * Record your answer in standard form (answer you see on the calculator)
0
700
Avogadro's number = 6.0221415 × 1023
The speed of light = 2.99 792 458 × 108 m / s
Temperature of the Sun's Core = 1.5 x 107 oC
since 15000000 kelvin = 14999726.85 degree Celsius
Distance related to Powers of 10
http://vimeo.com/819138
I picked 3 as my base
34
33
32
31
30
3 x 3 x 3 x 3
3 x 3 x 3 3 x 3 3 81
27
9
3
Try this
Evaluate each expression
*Image taken from "Math Makes Sense 9", page 59, copyright to pearson education Canada
a) 50
b) ­(5)0
c) (­5)0
d) ­50
Any number (except 0) with an exponent 0 will equal 1
20 = 1
130 = 1
1990 =1
(­6)0 = 1
Why???
Zero Exponent LAW
A power with an interger base, not including 0, and an exponent of 0 is equal to 1
PRACTICE TIME
A place value chart may help
Page 61­ 62
Write 96 713 as a power of 10
Erase to see solutions
96 713 = 90 000 + 6000 + 700 + 10 + 3
= (9 x 10 000) + (6 x 1000) + (7 x 100) + (1 x 10) + (3 x1)
= (9 x 104) + (6 x 103) + (7 x 102) + (1 x 101) + (3 x100)
# 4(a, b)
# 5(a, b, c, d)
#6(a, c, e)
#8( a, c, e)
#9(a, c, e) #10 all
#11
#13