# Important Questions Class 7 Mathematics Chapter 13

### Important Questions Class 7 Mathematics Chapter 13 – Exponents and Powers

Mathematics is an important subject taught in school. We need Mathematics to solve real-life problems such as those in construction, economy, medicine, etc.In this chapter, students will study exponents and powers.

It is a very important chapter because students will use powers and exponents. Students will study how to calculate the value of exponents and the multiplications and divisions of the same exponents. If a number is multiplied by itself, it can be expressed by the times it is being multiplied. The multiplication number is written at the right head of the number, called power. Students must practise questions from the chapter to score better in exams.

Extramarks is a leading company that provides students with all the important study materials, and our experts have made the Important Questions Class 7 Mathematics Chapter 13 to help students. They collected the questions from the textbook exercises, CBSE sample papers, CBSE past years’ question papers, and important reference books. They have also solved the questions, and experienced professionals have further checked the answers to ensure the best quality of the content. Thus, the question series will help students  score better.

Extramarks provides all the important study materials related to CBSE and NCERT. You can download the study materials after registering on our official website. We provide CBSE syllabus, CBSE sample papers, CBSE past years’ question papers, CBSE extra questions, CBSE revision notes, NCERT books, NCERT exemplars, NCERT solutions, NCERT important questions, vital formulas and many more.

### Important Questions Class 7 Mathematics Chapter 13 – With Solutions

The experts at Extramarks have provided the question series so that students can solve the questions regularly. They have taken help from various sources, such as the textbook exercise, CBSE sample papers, CBSE past years’ question papers, NCERT Exemplars, and important reference books. They have also solved the questions so that students can follow the answers. Our experienced professionals have further checked the solutions to ensure the best quality of the content. Thus, the Important Questions Class 7 Mathematics Chapter 13 will help students  score better in exams. The important questions are-

Question 1. What are the base, exponent, and value of the exponential form?

Answer 1. A base is a number that is to be multiplied by itself as per the exponent.

The exponent, or index, basically represents the number of times a base is to be multiplied by itself.

The product of the base with itself, according to the exponent, is the value of the exponential form.

Question 2. Identify the base, exponent, and value of the following:

• 25
• 34

• When a number is repeatedly multiplied by itself then it can be represented in an index or exponential notation. Like in 25

25 = 2 × 2 × 2 × 2 × 2 = 32.

In this equation, 2 is the base, 5 is the exponent or index and 32 is the value which is the fifth power of 2.

1. 34 = 81

Since it can be written as.

3 × 3 × 3 × 3 = 81

81 is the value of 3 to the power of 4.

Question 3. Calculate the value of the following:

• 26
• 93
• 112
• 54
• 24
• 52
• (4/7)3

Solution 3:

1. For 26 = 2 × 2× 2× 2× 2× 2 = 64

In this 2 is the base, 6 is the exponent and 64 is the value.

1. For 93 = 9 × 9 × 9 = 729

In this 9 is the base, 3 is the exponent and 729 is the value.

1. For 112 = 11 × 11 = 121

In this, 11 is the base, 2 is the exponent and 121 is the value.

1. For 54 = 5 × 5 × 5 × 5 = 625

In the, 5 is the base, 4 is the exponent and the value is 625.

1. For 24 = 2 × 2 × 2 × 2 = 16.

In this 2 is the base, 4 is the exponent and 16 is the value.

1. For 52 = 5 × 5 = 25

In this 5 is the base, 2 is the exponent and the value is 25.

1. In the given, 4/7 is the base and the exponent is 3. So to calculate the value,

47 × 47 × 47 = 64343

Question 4. Express the following in the exponential form:

• 6 × 6 × 6 × 6 × 6
• T × T × T
• 5 × 5 × 5 × 5 × 7 × 7 × 7 × 7× 7 × 7 × 7
• 4 × 4 × a × a
• a × a × a × a × b × b × b × c × c × c × c × c

1. The given question in the exponential form can be expressed as 65
2. The given question in the exponential form can be expressed as T3
3. The given question in the exponential form can be expressed as 54 × 77
4. The given question in the exponential form can be expressed as 42 × a2
5. The given question in the exponential form can be expressed as a4 × b3 × c5

Question 5. The numbers are given below. Express them using the exponential notation:

• 512
• 343
• 729
• 3125

1. In the exponential form, the number 512 can be expressed as 29

Because,

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

1. In the exponential form, the number 343 can be expressed as 73

Because,

343 = 7 × 7 × 7

1. In the exponential form, the number 729 can be expressed as 36

Because,

729 = 3 × 3 × 3 × 3 × 3 × 3

1. In the exponential form, the number 3125 can be expressed as 55

since  3125 = 5 × 5 × 5 × 5 × 5

Question 6. In the following, identify the greater number.

• 43 or 34
• 53 or 35
• 28 or 82
• 1002 or 2100
• 210 or 102

1. On expansion of 43, we get 4 × 4 × 4 = 64

On expansion of 34, we get 3 × 3 × 3 × 3 = 81

On comparing, it is clear that

64 < 81 or 43 < 3

So, the greater number here is 34

1. On expansion of 53, we get 5 × 5 × 5 = 125

On expansion of 35, we get 3 × 3 × 3 × 3 × 3 = 243

On comparing, it is clear that

125 < 243 or 53 < 35

So here the greater number is 35

1. On expansion of 28, we get 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

On expansion of 82, we get 8 × 8 = 64

On comparing, it is clear that

256 > 64 or 28 > 82 so the greater number is 28

1. On expansion of 1002, we get 100 × 100 = 10000

On expansion of 210, we get 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

So, by expansion of 2100, we get

1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024

So, it is very clear that

1002 < 2100

So, 2100 is the greater number.

1. The expansion of 210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

The expansion of 102 = 10 × 10 = 100

1024 > 100 so 210 > 102 so 210 is the greater number.

Question 7. Express the following as the product of the power of the prime factors.

• 648
• 405
• 540
• 3600

1. The factor of 648 can be presented as

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3 = 23 × 34

1. The factor of 405 can be presented as

405 = 3 × 3 × 3 × 3 × 5 = 34 × 5

1. The factor of 540 can be presented as

540 = 2 × 2 × 3 × 3 × 3 × 5 = 22 × 33 × 5

1. The factor of 3600 can be presented as

3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 24 × 32 × 52

Question 8: Simplify the following:

• 2 × 103
• 72 × 22
• 23 × 5
• 3 × 44
• 0 × 102
• 52 × 33
• 24 × 32
• 32 × 104

1. 2 × 103 can be written as 2 × 10 × 10 × 10 = 2 × 1000 = 2000
2. 72 × 22 can be written as 7 × 7 × 2 × 2 = 49 × 4 = 196
3. 23 × 5 can be written as  2 × 2 × 2 × 5 = 8 × 5 = 40
4. 3 × 44 can be written as 3 × 4 × 4 × 4 × 4= 3 × 256 = 768
5. 0 × 102  can be written as 0 × 10 × 10 = 0 × 100 = 0
6. 52 × 33 can be written as 5 × 5 × 3 × 3 × 3 = 25 × 27 = 675
7. 24 × 32 can be written as 2 × 2 × 2 × 2 × 3 × 3 = 16 × 9 = 144
8. 32 × 104 can be written as 3 × 3 × 10 × 10 × 10 × 10 = 9 × 10000 = 90000

Question 9. Simplify the following given below:

• (-4)3
• (-3) × (-2)3
• (-3)2 × (-5)2
• (-2)3 × (-10)3

1. On expansion of (-4)3,

We get

-4 × -4 × -4 = -64

1. On expansion of (-3) × (-2)3

We get

-3  × -2 × -2 × -2 = -3 × -8 = 24

1. On expansion of (-3)2 × (-5)2

We get -3 × -3 × -5 × -5 = 9 × 25 = 225

1. On expansion of (-2)3 × (-10)3

We get

-2 × -2 × -2 × -10 × -10 × -10 = -8 × -1000 = 8000

Question 10. Compare the following numbers:

• 2.7 × 10 12 and 1.5 × 108
1. b) 4 × 1014 and 3 × 1017

a)The above equation is given as 2.7 × 10 12 and 1.5 × 108

On comparison made for the exponents of base 10, we get

2.7 × 10 12 > 1.5 × 108

1. b)       The above equation is given as 4 × 1014 and 3 × 1017

On comparing the exponents of base 10, we will clearly find that

4 × 1014 < 3 × 1017

Question 11. What are the laws of the exponent?

Answer 11: The laws of exponents make the expression of the exponential form simplified.

As per product law,

• When the bases are the same and the exponents are different then the product law is expressed as

am × an = a m+n

in this a is a rational number while m and n are the natural numbers

• The other aspect of product law is when the bases are different but the exponents are the same then the product law is:

an × bn = (ab)n

here a and b are the rational numbers while n is a natural number.

As per quotient law,

• When the bases are the same but the exponents are different then as per quotient law,

am ÷ an = am-n

here a is the rational number and m and n are the natural numbers.

• When the bases are different and the exponents are the same, then the quotient law is an ÷ bn = (a/b)n. here a and b are the rational number and n is a natural number.

As per power law,

If a is a rational number and m, n are natural numbers then according to the power law, (am)n = amn

Question 12. Simplify the given equation below and write the answer in the exponential form. Use laws of exponents.

• 32 × 34 × 38
• 615 ÷ 610
• a3 × a2
• 7x × 72
• (52)3 ÷ 53
• 25 × 55
• b4 × c4
• (34)
• (220 ÷ 215) × 23

1. 32 × 34 × 38 will be written as (3) 2 + 4 + 8 = 314

The above is related to the rule of multiplying the powers when they have the same base

Like am × an = a m+n

1. 615 ÷ 610 will be written as (6) 15-10 = 65

The above is related to the rule of dividing the power which have the same base.

Like am ÷ an = a m-n

1. a3 × a2 will be written as (a) 3 + 2 = a5.

The above is related to the rule of multiplying the powers when they have the same base

Like am × an = a m+n

1. 7x × 72 will be written as 7 (x + 2), this is in accordance with the rule of multiplying the powers when they have the same base, like am × an = a m+n
1. (52)3 ÷ 53. In this the rule of power of as power will be followed, according to which

(am)n = a mn

Following this, (52)3 ÷ 53 will be written as:

(52)3 = (5)2 × 3 = 56

Final equation here will be 56 ÷ 53. To solve this, following the rule of dividing the power which have the same base is am ÷ an = a m-n

= (5)6-3 = 53

1. 25 × 55 = (2 × 5)5 = 105. The rule of multiplying the power with the same exponent is applied here.
1. b4 × c4 = (b × c)4 = bc4. The rule of multiplying the power with the same exponents is applied here.
1. (34)3 = (3) 4× 3 = 312. The rule of taking the power of as power is applied here.
1. (220 ÷ 215) × 23

First of all, the rule of dividing the power with the same base will be applied,

So (220 ÷ 215) will be further simplified as (2) 20-15 = 25

After this,

The rule of multiplying the power with the same base will be applied

am × an = am+n

So 25 × 23 will be simplified and written as

(2)5+3 = 28

Question 13. The statements given below have numbers. Express them in the standard form.

1. The distance between the earth and the moon is 384,000,000 m
2. In a vacuum, the speed of light is 300, 000, 000 m/s
3. The earth has a diameter of 1,27,56,000 m
4. The sun has a diameter of 1,400,000,000 m
5. The average number of stars present in the galaxy is 100,000,000,000.
6. The age of the universe is estimated to be around 12,000,000,000 years old.
7. 300,000,000,000,000,000,000 m is the distance of the sun estimated from the centre of the milky way galaxy.
8. A drop of water weighing 1.8 gm has 60,230,000,000,000,000,000,000 molecules contained in it.
9. It is estimated that the earth has 1,353,000,000 cubic km of seawater.
10. In the year 2001, in March, India had a population of 1,027,000,000

The numbers given in the statement will be expressed as:

1. 3.84 × 108 m
2. 3 × 108 m/s
3. 1.2756 × 107 m
4. 1.4 × 109 m
5. 1 × 1011 stars
6. 1.2 × 1010 years old
7. 3 × 1020 m
8. 6.023 × 1022 molecules
9. 1.353 × 109 cubic km
10. 1.027 × 109

Question 14. The numbers are given below. Express them in the standard form.

• 5,00,00,000
• 70,00,000
• 3,18,65,00,000
• 3,90,878
• 39087.8
• 3908.78

1. The standard form of 5,00,00,000 is 5 × 107
2. The standard form of 70,00,000 is 7 × 106
3. The standard form of 3,18,65,00,000 is 3.1865 × 109
4. The standard form of 3,90,878 is 3.90878 × 105
5. The standard form of 3,9087.8 is 3.90878 × 104
6. The standard form of 3908.78 is 3.90878 × 103

Question 15. Write the given number in the expanded form.

• (8 × 10)4 + (6 × 10)3 + (0 × 10)2 + (4 × 10)1 + (5 × 10)0
• (4 × 10) 5 + (5 × 10)3 + (3 × 10)2 + (2 × 10)0

1. The expanded form of the given number will be presented as:

(8 × 10000) + (6 × 1000) + (0 ×100) + (4 × 10) + (5 × 1) = 80000 + 6000+ 0 + 40 + 5 = 86045

1. The expanded form of the given number will be presented as:

(4 × 100000) + (0 × 10000) + (5 × 1000) + (3 × 100) + (0 × 10) + (2 ×1) = 400000 + 5000 + 300 + 2 = 405302

Question 16. Write the following numbers given below in the expanded form:

• 279404
• 3006194
• 2806196
• 120719
• 20068

1. The expanded form of 279404 is:

(2 × 100000) + (7 × 10000) + (9 × 1000) + (4 × 100) + (0 × 10) + (4 × 1)

The above can be presented as the power of 10 in the exponential form

(2 × 105) + (7 × 104) + (9 × 103) + (4 × 102) + (0 × 101) + (4 × 100)

1. The expanded form of 3006194 is:

(3 × 1000000) + (0 × 100000) + (0 × 10000) + (6× 1000) + (1 × 100) + (9 × 10) + 4

The above can be presented as the power of 10 in the exponential form

(3 × 106) + (0 × 105) + (0 × 104) + (6 × 103) + (1 × 102) + (9 × 101) + (4 × 100)

1. The expanded form of 2806196 is

(2 × 1000000) + (8 × 100000) + (0 × 10000) + (6× 1000) + (1 × 100) + (9 × 10) + 6

The above can be presented as the power of 10 in the exponential form

(2 × 106) + (8 × 105) + (0 × 104) + (6 × 103) + (1 × 102) + (9 × 101) + (6 × 100)

1. The expanded form of 120719 is

(1 × 100000) + (2 × 10000) + (0 × 1000) + (7 × 100) + (1 × 10) + (9 × 1)

The above can be presented as the power of 10 in the exponential form

(1 × 105) + (2 × 104) + (0 × 103) + (7 × 102) + (1 × 101) + (9 × 1010)

1. The expanded form of 20068 is

(2 × 10000) + (0 × 1000) + (0 × 100) + (6× 10) + (8 × 1)

The above can be presented as the power of 10 in the exponential form

(2 × 104) + (0 × 103) + (0 × 102) + (6 × 101) + (8 × 100

Question 17. Identify which of the following is positive or negative.

• (-5)11
• (-3)20
• (-8)113
• (-5)40
• (-8)0
• (-7)-5
• (-110)-40

 Expression Positive/negative Reason of the interpretation (-5)11 Negative The exponent is odd (-3)20 Positive The exponent is even (-8)113 Negative The exponent is odd (-5)40 Positive The exponent is even (-8)0 Positive The exponent is even (-7)-5 Negative The exponent is odd (-110)-40 Positive The exponent is even

### Benefits of Solving Important Questions Class 7 Mathematics Chapter 13

Practice is very important for students to score well in exams. There are multiple benefits of the practice. It helps students  generate interest in the subject matter and boost their confidence.It is critical to begin practising with students in early classes. The experts have made the Important Questions Class 7 Mathematics Chapter 13 to help students in practice. The benefits of solving the questions are-

•       Students need more than the textbook exercises because the exercises have limited questions. Now, they would need help to search for questions in different books. Our experts have done the job for them, and they have collected the questions from different sources. They have taken help from the textbook exercise, CBSE sample papers, CBSE past years’ question papers, NCERT exemplar and important reference books. Thus, the Class 7 Mathematics Chapter 13 Important Questions provides a wide range of questions so that students can be better prepared for the exams.
•      The experts have not only collected the questions, but they have also solved the questions so that students can follow the answers. They explained the questions and provided a step-by-step process to explain each question. Hence, students can take help from the experts’ solutions and check their answers. Experienced professionals have further checked the answers to ensure the best quality of the content. Thus, the Mathematics Class 7 Chapter 13 Important Questions will help students  score better in exams.
•    The experts have tried to cover the whole chapter and every important concept. They have taken help from as many sources as possible to include the maximum types of questions. Thus, students will be well prepared for the exams. The practise will boost their confidence in the subject. Many students tend to fear mathematics because they have problems understanding it. Practice can reduce their fear of Mathematics and help  generate interest in the subject matter. Thus, the Chapter 13 Class 7 Mathematics Important Questions will help students better understand the subject matter.

Extramarks is a leading company that provides all the important study materials related to CBSE and NCERT. You must register on our official website and download the study materials. We provide CBSE syllabus, CBSE sample papers, CBSE past years’ question papers, CBSE revision notes, CBSE extra questions, NCERT books, NCERT exemplars, NCERT important questions, NCERT solutions, vital formulas, and many more. Like the Important Questions Class 7 Mathematics Chapter 13, you can also find important questions for other chapters. The links to the study materials are given below-

• NCERT books
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