Class 7 Maths Chapter 13 Exercise 13.1 Pdf Notes NCERT Solutions

Class 7 Maths Chapter 13 Exponents And Power Exercise 13.1 pdf notes:-

• Exercise 13.1
• Exercise 13.2
• Exercise 13.3

Exercise 13.1 Class 7 maths Chapter 13 Pdf Notes:-

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Ncert Solution for Class 7 Maths Chapter 13 Exponents And Power Exercise 13.1 Tips:

INTRODUCTION
Do you know what the mass of earth is? It is
5,970,000,000,000,000,000,000,000 kg!
Can you read this number?
Mass of Uranus is 86,800,000,000,000,000,000,000,000 kg.
Which has greater mass, Earth or Uranus?
Distance between Sun and Saturn is 1,433,500,000,000 m and distance between Saturn
and Uranus is 1,439,000,000,000 m. Can you read these numbers? Which distance is less?
These very large numbers are difficult to read, understand and compare. To make these
numbers easy to read, understand and compare, we use exponents. In this Chapter, we shall
learn about exponents and also learn how to use them.

EXPONENTS
We can write large numbers in a shorter form using exponents.
Observe 10, 000 = 10 × 10 × 10 × 10 = 104
The short notation 104

stands for the product 10×10×10×10. Here ‘10’ is called the

base and ‘4’ the exponent. 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.

We can similarly express 1,000 as a power of 10. Note that

1000 = 10 × 10 × 10 = 103

Here again, 103

is the exponential form of 1,000.
Similarly, 1,00,000 = 10 × 10 × 10 × 10 × 10 = 105
105 is the exponential form of 1,00,000
In both these examples, the base is 10; in case of 103

, the exponent

is 3 and in case of 105

the exponent is 5.

We have used numbers like 10, 100, 1000 etc., while writing numbers in an expanded
form. For example, 47561 = 4 × 10000 + 7 × 1000 + 5 × 100 + 6 × 10 + 1
This can be written as 4 × 104 + 7 ×103

• 5 × 102
• 6 × 10 + 1.
  Try writing these numbers in the same way 172, 5642, 6374.
  In all the above given examples, we have seen numbers whose base is 10. However
  the base can be any other number also. For example:
  81 = 3 × 3 × 3 × 3 can be written as 81 = 34

, here 3 is the base and 4 is the exponent.

Some powers have special names. For example,
102
, which is 10 raised to the power 2, also read as ‘10 squared’ and
103
, which is 10 raised to the power 3, also read as ‘10 cubed’.
Can you tell what 53

(5 cubed) means?
53 = 5 × 5 × 5 = 125
So, we can say 125 is the third power of 5.
What is the exponent and the base in 53
?

Similarly, 25

= 2 × 2 × 2 × 2 × 2 = 32, which is the fifth power of 2.
In 25
, 2 is the base and 5 is the exponent.
In the same way, 243 = 3 × 3 × 3 × 3 × 3 = 35
64 = 2 × 2 × 2 × 2 × 2 × 2 = 26
625 = 5 × 5 × 5 × 5 = 54

Try These Find five more such examples, where a number is expressed in exponential form.
Also identify the base and the exponent in each case.

You can also extend this way of writing when the base is a negative integer.
What does (–2)3
mean?
It is (–2)3

= (–2) × (–2) × (–2) = – 8
Is (–2)4 = 16? Check it.
Instead of taking a fixed number let us take any integer a as the base, and write the
numbers as,
a × a = a2
(read as ‘a squared’ or ‘a raised to the power 2’)
a × a × a = a3 (read as ‘a cubed’ or ‘a raised to the power 3’)
a × a × a × a = a4 (read as a raised to the power 4 or the 4th power of a)
…………………………
a × a × a × a × a × a × a = a7

(read as a raised to the power 7 or the 7th power of a)

and so on.
a × a × a × b × b can be expressed as a3
b2
(read as a cubed b squared)