EXPONENTS

1
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

2
Exponents

• We can write large numbers in a shorter form
  using exponents
• 10,00010x10x10x104
• 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.

3
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.

4
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

5
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
• 2 x 2 x 2
• 8
• 2 is a factor 3 times
• 2 x 2 x 2 x 2
• 16
• 2 is a factor 4 times
• 2 x 2 x 2 x 2 x 2
• 32
• 2 x 2 x 2 x 2 x 2 x 2
• 64
• 2 is a factor 6 times
• 2 is a factor 5 times
• 2 x 2 x 2 x 2 x 2 x 2 x 2
• 128

6
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

7

• 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.

8

• 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

9
Exercises

• Express
• 729 as a power of 3
• 128 as a power of 2
• 343 as a power of 7

10
Questions

• 2) Find the value of
• A) 2²
• B) 9³