Download UNIT 2 : POWERS 2.1 What`s a power? It is a number obtained by

UNIT 2 : POWERS
2.1 What’s a power?
It is a number obtained by multiplying a number by itself a certain number
of times
2X2X2X2X2X2
.
We have 2 multiplied by itself six times, so we can write it in exponential
notation.
2X2X2X2X2X2= 2 6
2 is the base and 6 is the exponent.
The value of 2 6 = 64
Be careful ! 2 6  2x6
Exercise:
Index or
Exponent
READ AS
EXTENDED
VALUE
Four squared
or
Four to the power of two
4x4
16
BASE NUMBER
4
5
2
3
10
4
Five cubed
or
Five to the power of three
Ten to the power of four
5x5x5
10x 10x10x10
125
10.000
63
16
Seven cubed or
2x2x2x2x2
8x8
Two to he power of six
2.2. Powers of 10
"Powers of 10" is a very useful way of writing down large or small numbers.
Instead of having lots of zeros, you show how many powers of 10 will make
those many zeros
Example: 5.000 = 5 × 1.000 = 5 × 103
5 thousand is 5 times a thousand. And a thousand is 103. So 5 times
103 = 5.000
Can you see that 103 is a handy way of making 3 zeros?
Scientists and Engineers (who often use very big or very small numbers)
like to write numbers this way. It is commonly called Scientific Notation,
or Standard Form.
Example: The Mass of the Sun
The Sun has a Mass of 1,988 × 1030 kg.
It would be too hard for scientists to write
1.988.000.000.000.000.000.000.000.000.000 kg
(And very easy to make a mistake counting the zeros!)

The Trick
While at first it may look hard, there is an easy "trick":
The index of 10 says ...
... how many places to move the decimal point to the right.
Example: What is 1.35 × 104 ?
You can calculate it as: 1,35 x (10 × 10 × 10 × 10) = 1,35 x 10.000 = 13.500
But it is easier to think "move the decimal point 4 places to the right" like
this:
1,35
13,5
135
1350
13500
Exercise:
a) Write 3,76 × 104 as an ordinary number
b) Write 718.000 in Scientific notation
2.3 Laws of Powers ( Rules of Powers)
Law
· an = am+n
am/an = am-n
(am)n = am· n
am · bm = (a · b) m
an:bn = (a:b)n
am
Example
· 33 = 32+3 = 35
26/22 = 26-2 = 24
(42)3 = 42×3 = 46
23· 33 = (2· 3 )3 = 63
(5:3)2 = 52 : 32
32
ACTIVITIES
1. Write in exponential notation
a) 7 · 7 =
d) 4 · 4 · 4 · 4 =
b) 3 · 3 · 3 · 3 · 3 · 3 =
e) 8 · 8 · 8 =
c) 10 · 10 · 10 · 10 =
f) 2 · 2 · 2 · 2 · 2 · 2 =
2. Complete:
m ·m·m  m
b) x · x  x
a)
e)
c) a · a · a =
d) …………………….. = b
Power
3
Base
Exponent
5
m
3
5
4
7
a4
Find the value of :
3.
2
4.Find the missing number:
8
3
2x  4
5
8 x  512
94
15 2
3 x  81
12 3
30 4
a 4  16
20 5
85 2
a 3  1.000
100
3
324
10 x  10.000
a  25
2
2
6 x  36
a 3  125
5. a) Write 4,015 × 105 as an ordinary number.
b) The diameter of the Earth is 12.756,2 kilometers. Write it in Scientific Notation.
c) Write 7,0678 x 10 as an ordinary number.
d) Write 727.000.000.0000 in scientific notation
8
6. Express the result as a power and then find the value:
18 2 : 9 2
6 3 · 53
6 5 : 35
53 · 2 3
2 6 · 56
46 : 26
20 4 : 5 4
16 5 : 8 5
4 3 · 53
15 3 : 5 3
25 3 · 4 3
214 : 3 4
54 · · 24
82 · 52
84 : 44
35 2 : 5 2
7. Express the result as a power:
a) ( 2 5 · 35 ) : 6 5
b) ( 6 4 · 34 ) : 9 4
c) ( 80 3 : 83 ) : 53
8. Work out:
3 2 · 35
m7 · m
26 : 22
10 7 : 10 6
1210 : 12 9
x2 · x6
52 · 52
38 : 3 5
a 10 : a 6
k7 · k6
10 5 · 10 2
a · a5
m5 : m
x8 : x 4
510 : 5 6
9. Operate:
( 52 )3
( 25 ) 2
( x 2 )3
( 10 3 ) 3
( a 3 )5
( 83 ) 7
( m6 )2
( x4 )4
( 7 4 )3
10. Work out:
z9 : z9
x8 : x7
a9 : a2
k 12 : k 9
z9 · z
x8 · x0
a5 · a5
k3 · k
( z8 )4
( x3 )2
( a 5 )3
11. Express the result as a power:
5 · 4  : 2
15 : 5  : 3
36 : 2 · 9 
3
3
3
5
5
4
4
3
4

6 3 : 213 : 7 3
2
4

( k 9 )2
a  : a
m  : m 
x : x · x

3 4
4 3
· 2 5 : 29


12 9 : 4 7 · 3 7
10 5
3
5 2
2
4
: x3

CHECK YOURSELF
1.Calculate mentally and write in words the following powers:
a) 4 3 
b) 112 
c) 5 3 
d ) 10 2 
e) 100 3 
2. Complete:
POWER
READ AS
Seven to the power of four
EXTENDED
VALUE
100.000
10 7
64
18
3x3x3x3x3
3. Fill in the missing numbers.
a) 7 5 · 7 2  7
e) 912 : 9 2  9
b) 6 6 · 6 8  6
c) 4 3 ·
3
4
d ) 54 · · 5  5
i ) 18 2 : 9 2  2
f ) 26 : 2  22
j) 2 6 · 56 
g ) 24 7 : 3  24 4
k )  43
h)
4·
2
:
 52
e) 2 3 : 2 7 
b) 4 6  4 2 
b) 7 6 · 7 2 
 
3
c) x 4  x 3 
 
c) 3 4
5
: 33 
4  4
l ) 5 4 · · 2 4  10
4.Express the result as a power:
a) a 3  a  a 7 
6
d)
d)
a6  a4

a3
a6  a4 · a9

a2