Transcript EXPONENTS & POWERS

EXPONENTS & POWERS
 It becomes difficult to read, understand and compare very
large numbers. To make these numbers easy to read,
understand and compare, we use exponents.
 Mass of earth is 5,976,000,000,000,000,000,000,000 kg
 Mass of Uranus is 86,800,000,000,000,000,000,000 kg
 Distance between Sun and Saturn is :-1,433,500,000,000m
 Distance between Saturn & Uranus is 1,439,000,000,000m
Exponents
 We can write large numbers in a shorter form
using exponents
 10,000=10x10x10x104
 The short notation 104 stands for the product 10 x
10 x 10 x 10. Here “10” is called the base and
'The number 104 is read as 10 raised to the power
of 4 or simply as fourth power of 10. 104 is
called the exponential form of 10,000.
Exponents
We can also express 1000 as power of 10.
Since 1000 is 10 multiplied by itself 3
times.
1000 = 10 x 10 x 10 = 103
We must write the numbers repeatedly
multiplied as base and number of times it is
multiplied as the power.
Exponents
 When the negative number is raised to an even
power the value is always is positive.
 When the negative number is raised to an odd
number the value is always negative.
 Very large numbers can be expressed as products
of suitable powers of ten.
 When ‘0’ is multiplied by 10, the product is zero.
(0) When ‘Zero’ is added to any number the
value of that number remains the same.
Therefore 24005 can be written as ;
24005 = 2 x 104 + 4 x 103 + 5 x 102
Exponents – factors
 In the table below, the number 2 is written as a factor repeatedly. The
product of factors is also displayed in this table. Suppose that your
teacher asked you to Write 2 as a factor one million times for
homework. How long do you think that would take? Answer
 Factors Product of FactorsDescription2 x 2 =
 4
 2 is a factor 2 times
 2x2x2=
 8
 2 is a factor 3 times
 2x2x2x2=
 16
 2 is a factor 4 times
 2x2x2x2x2=
 32
Exponents – factors of 2
 2 is a factor 5 times
 2 x 2 x 2 x 2 x 2 x 2 = 64
 2 is a factor 6 times
 2 x 2 x 2 x 2 x 2 x 2 x 2 =128
 2 is a factor 7 times
 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 =256
 2 is a factor 8 times
Writing 2 as a factor one million times
would be a very time-consuming and
tedious task. A better way to approach
this is to use exponents. Exponential
notation is an easier way to write a
number as a product of many factors.
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Solution:
Write 3 x 3 x 3 x 3 using exponents, then read your answer aloud.
3 x 3 x 3 x 3 = 34
3 raised to the fourth power
Example 3:
Write 6 x 6 x 6 x 6 x 6 using exponents, then read your answer aloud.
Solution:
6 x 6 x 6 x 6 x 6 = 65
Example 2:
6 raised to the fifth power
Example 4:
Write 8 x 8 x 8 x 8 x 8 x 8 x 8 using exponents, then read your answer aloud.
Solution:
8 x 8 x 8 x 8 x 8 x 8 x 8 = 87
8 raised to the seventh power
Exercises
1. Express :
729 as a power of 3
ii) 128 as a power of 2
iii) 343 as a power of 7
i)
Questions
2) Find the value of :
A) 2²
B) 9³