VMC VIQ Scholarship Test
ApplyRegister for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.
NCERT Solutions for Exponents And Powers Class 7 - If someone asks you about the speed of bus or car, you may say its 40 km/hr but if you have asked about the speed of light in a vacuum, you will say its approximately 300,000,000 m/s. This is a very big number which is very difficult to write, interpret, and handle. To make any number to represent in an easy way there is a system called exponents. In this article, you will get CBSE NCERT solutions for Class 7 Maths chapter 13 Exponents and Powers.
Exponents can be used to represent very large numbers and small numbers as the power of a base number. In the above example, you can write 300,000,000 m/s as . Important topics like laws of exponents, multiplying and dividing the power with the same base, multiplying and dividing the powers with the same exponents and expressing large numbers in the standard form are covered in NCERT. There are many questions from the above topics in the solutions of NCERT for Class 7 Maths chapter 13 Exponents and Powers that are explained in a step-by-step manner. It will be very easy for you to understand the concepts. In this chapter, there are 17 questions in the 3 exercises of the NCERT textbook. You will get detailed explanations of all these questions in the NCERT Solutions for Class 7 . Check NCERT Solutions from Classes 6 to 12 by clicking on the above link. Here you will get solutions to three exercises of this chapter.
am × an = am+n
am ÷ an = am-n
( am )n = amn
am × bm = (ab)m
am ÷ bn = (a÷b)m
a0 = 1 ( a, non-zero integer)
(-)even number = 1
(-)odd number = -1
Exponents: Exponents represent repeated multiplication of a number (base) by itself.
x4 where x is the base and 4 is the exponent. It is read as x raised to the power of 4 or fourth power of x.
Understanding Powers of 10:
Free download NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers PDF for CBSE Exam.
Question:(i) Express:
729 as a power of 3
Answer:
729 as a power of 3 is given as
Question: 1(i) Find the value of:
Answer:
the value of is given by
Question: 1(iv) Find the value of:
Answer:
the value of is given by
Question: 2 Express the following in exponential form:
Answer:
can be given as
.
can be given as .
can be given as .
can be given as
.
can be given as
.
can be given as
.
Question: 3 Express each of the following numbers using exponential notation:
(i) 512 (ii) 343 (iii) 729 (iv) 3125
Answer:
(i) 512
2 | 512 |
2 | 256 |
2 | 128 |
2 | 64 |
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
(ii) 343
7 | 343 |
7 | 49 |
7 | 7 |
1 |
(iii)729
3 | 729 |
3 | 243 |
3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
(iv)3125
5 | 3125 |
5 | 625 |
5 | 125 |
5 | 25 |
5 | 5 |
1 |
Question: 4 Identify the greater number, wherever possible, in each of the following?
Answer:
since
is greater than
since
is greater than
since
is greater than
since
is greater than
since
is greater than
Question: 5 Express each of the following as product of powers of their prime factors:
(i) 648 (ii) 405 (iii) 540 (iv) 3,600
Answer:
(i) 648
2 | 648 |
2 | 324 |
2 | 162 |
2 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
(ii) 405
5 | 405 |
3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
(iii)540
2 | 540 |
2 | 270 |
3 | 135 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
(iv) 3600
2 | 3600 |
2 | 1800 |
2 | 900 |
2 | 450 |
3 | 225 |
3 | 75 |
5 | 25 |
5 | 5 |
1 |
Question: 6(i) Simplify:
Question: 8 Compare the following numbers:
Answer:
on comparing exponents of base 10.
on comparing exponents of base 10.
Question:(i) Simplify and write in exponential form:
Answer:
can be simplified as
Question: 1 Simplify and write in exponential form: (eg., )
Answer:
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
Question: Simplify and write the answer in exponential form:
Answer:
can be simplified as
can be simplified as
can be simplified as
can be simplified as
Question: Put into another form using :
Answer:
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
Question: Put into another form using :
Answer:
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
Question: 1 Using laws of exponents, simplify and write the answer in exponential form:
Answer:
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
can be simplified as
Question:2(i) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(ii) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(iii) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(iv) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(v) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(vi) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(vii) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(viii) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(ix) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(x) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 2(xi) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question:2(xii) Simplify and express each of the following in exponential form:
Answer:
can be simplified as
Question: 3 Say true or false and justify your answer:
Answer:
can be simplified as
Since ,
Thus, it is false
can be simplified as
Since,
Thus, it is false
can be simplified as
Since ,
Thus, it is false
can be simplified as
Since, LHS = RHS
Thus, it is true.
Question: 4 Express each of the following as a product of prime factors only in exponential form:
Answer:
2 | 108 |
2 | 54 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
2 | 192 |
2 | 96 |
2 | 48 |
2 | 24 |
2 | 12 |
2 | 6 |
3 | 3 |
1 |
2 | 270 |
3 | 135 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
3 | 729 |
3 | 243 |
3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
2 | 64 |
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
2 | 768 |
2 | 384 |
2 | 192 |
2 | 96 |
2 | 48 |
2 | 24 |
2 | 12 |
2 | 6 |
3 | 3 |
1 |
Question: Expand by expressing powers of 10 in the exponential form:
(i) 172 (ii) 5,643 (iii) 56,439 (iv) 1,76,428
Answer:
(i) 172
(ii) 5,643
(iii) 56,439
(iv) 1,76,428
Question: 1 Write the following numbers in the expanded forms:
279404, 3006194, 2806196, 120719, 20068
Answer:
(i) 279404
(ii) 3006194
(iii) 2806196
(IV) 120719
(V) 20068
Question: 2 Find the number from each of the following expanded forms:
Answer:
Thus, the above problems are simplified in simpler forms.
Question: 3 Express the following numbers in standard form:
(i) 5,00,00,000 (ii) 70,00,000 (iii ) 3,18,65,00,000 (iv) 3,90,878 (v) 39087.8 (vi) 3908.78
Answer:
(i) 5,00,00,000
(ii) 70,00,000
(iii ) 3,18,65,00,000
(iv) 3,90,878
(v) 39087.8
(vi) 3908.78
Question: 4 Express the number appearing in the following statements in standard form.
(a) The distance between Earth and Moon is 384,000,000 m.
(b) Speed of light in vacuum is 300,000,000 m/s.
(c) Diameter of the Earth is 1,27,56,000 m.
(d) Diameter of the Sun is 1,400,000,000 m.
(e) In a galaxy there are on an average 100,000,000,000 stars.
(f) The universe is estimated to be about 12,000,000,000 years old.
(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
(i) The earth has 1,353,000,000 cubic km of sea water.
(j) The population of India was about 1,027,000,000 in March, 2001.
Answer:
(a) The distance between Earth and Moon = 384,000,000 m
(b) Speed of light in vacuum =300,000,000 m/s.
(c) Diameter of the Earth = 1,27,56,000 m.
(d) Diameter of the Sun = 1,400,000,000 m.
(e) In a galaxy there are on an average = 100,000,000,000 stars.
(f) The universe is estimated to be about= 12,000,000,000 years old.
(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated = 300,000,000,000,000,000,000 m.
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
60,230,000,000,000,000,000,000
(i) The earth has 1,353,000,000 cubic km of seawater.
(j) The population of India was about 1,027,000,000 in March 2001.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | Exponents and Powers |
Chapter 14 | |
Chapter 15 |
For any non-zero integers, a and b and whole numbers m and n it obey certain properties given below
Tip- If you understood the fundamental of this chapter, you don't need to remember above these findings. You can simply derive these properties by the strong fundamentals of this chapter. You should try to solve all the NCERT questions including the practice questions given at the end of every topic. You can take help from the CBSE NCERT solution for class 7 maths chapter 13 exponents and powers if you are facing difficulties while solving the problems.
Happy Reading!!!
Also Check NCERT Books and NCERT Syllabus here:
Admit Card Date:04 October,2024 - 29 November,2024
Admit Card Date:04 October,2024 - 29 November,2024
Application Date:07 October,2024 - 22 November,2024
Application Correction Date:08 October,2024 - 27 November,2024
Register for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
Accepted by more than 11,000 universities in over 150 countries worldwide
Register now for PTE & Unlock 20% OFF : Use promo code: 'C360SPL20'. Valid till 30th NOV'24! Trusted by 3,500+ universities globally
As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE