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Published on: 05/12/2018
CBSE Class 7 is a crucial grade in your secondary school education. So learning with effective preparation is a must. Our study materials for CBSE Class 7 follow the latest CBSE syllabus and are prepared by subject experts who have much experience in the academic industry. In this question paper, the questions are cover from the 7th Maths chapter Exponents and Powers. Questions are prepared as per NCERT guidelines by the help of expert teachers.
By referring to our solutions, students get a clear understanding of each concept in detail. Students who have referred to our solutions have seen a significant increase in overall marks and ease in understanding the subjects. Our study materials are not only used by students but also by educational institutes in India.
In this post, we are providing you with the most important questions of Maths exam from the chapter Exponents and Powers. You should know answers to these questions in all likelihood to score good marks in Class 7 Maths exam.
The latest sample papers have been designed as per the latest blueprints, syllabus and examination trends. Sample papers should be practiced in examination condition at home or school and also show it to your teachers for checking or compare with the answers provided.
Download CBSE Class 7th Standard CBSE Mathematics question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 7th Standard CBSE Mathematics
Questions + Answers key
Take MCQ Mathematics Test
1.
Can you write the appropriate number in the box
d10 x d20=d◻️
2.
Find the value of:
(-3)4
3.
Write in the exponential form:
625
4.
Dividing the Powers with the Same Exponents
(-3)2 \(\div\) p2
5.
Find the value of \(\frac{3^7}{3^4\times 3^3}\times 9\)
6.
Write I x I x I x I x I x m x m x m in the exponential form.
7.
Write the following numbers in the expanded forms: 3006194
8.
Express each of the following in single exponential form.
(-3)3 x (-10)3
9.
Simplify the following expression and write the answer in exponential form: \(\frac { { 2 }^{ 8 }\times { 5 }^{ 4 }\times { 4 }^{ 3 } }{ { 2 }^{ -2 }\times { 5 }^{ -6 }\times { 4 }^{ 3 } } \)
10.
Using laws of exponents, simplify and write the answer in exponential form: 32 x 34 x 38
11.
Using the laws of exponents, solve the following: 25 X 27
12.
Write the reciprocal of the following rational numbers. \(-\frac { 7 }{ 11 } \)
13.
Simplify 0 x102
14.
Express each of the following numbers using exponential notation: 512
15.
Find the value of 26
16.
100000000000 in standard form is
1 x 108
1 x 109
1 x 1010
1 x 1011
17.
30 + 40 + 50=
1
2
3
none of these
18.
1f 23 x 24 = 2?, then? =
3
4
1
7
19.
What is the base in 82?
8
2
6
10
20.
The exponential form of 64 is
25
26
27
28
21.
For an!, two non-zero rational numbers x and y, x5 \(\div\) y5 is equal to :
(x \(\div\) y)1
(x \(\div\) y)0
(x \(\div\) y)5
(x \(\div\) y)10
22.
Example 2 : (-7)5 x (-7)3 is equal to
(-7)8
-(7)8
(-7)15
(-7)2
23.
If \(\frac { p }{ q } =\left( \frac { 5 }{ 6 } \right) ^{ 2 }\div \left( \frac { 5 }{ 6 } \right) ^{ 0 }\), then the value of \(\left( \frac { p }{ q } \right) ^{ 2 }\) is
\(\frac { 125 }{ 1290 } \)
\(\frac { 625 }{ 1296 } \)
\(\frac { 164 }{ 125 } \)
\(\frac { 169 }{ 144 } \).
24.
\(\left[ \{ \left( \frac { 2 }{ -9 } \right) ^{ 2 }\} ^{ 0 } \right] ^{ 2 }\) is equal to
2
\(\frac { 4 }{ 81 } \)
\(\frac { 81 }{ 4 } \)
1
25.
The reciprocal of \(\left( \frac { -2 }{ 5 } \right) ^{ 2 }\) is
\(\left( \frac { -5 }{ 2 } \right) ^{ 2 }\)
\(\left( \frac { 5 }{ 2 } \right) ^{ 2 }\)
\(\frac { 4 }{ 25 } \)
\(\frac { 25 }{ 4 } \)
26.
The distance between Sun and Earth is 149,600,000,000m.lts standard form is______________ m.
27.
\(({1\over3})^4\)is expressed in product form as ________________
28.
\(({6\over 7})^5 \div ({6\over 7})^3=\)___________
29.
10000 _____ 105
30.
88880000000 = ........ x 1010
31.
\(\left( \frac { 11 }{ 15 } \right) ^{ 4 }\times (......)^{ 5 }=\left( \frac { 11 }{ 15 } \right) ^{ 9 }\)
32.
\(\left( \frac { 5 }{ 8 } \right) ^{ 9 }\times \left( \frac { 5 }{ 4 } \right) ^{ 4 }=\left( \frac { 5 }{ 8 } \right) ^{ 4 }\)
33.
xm + xm = x2m where x is a non-zero rational number and m is a positive integer.
34.
9001006001 =9 x 109 + 1 x 106 + 6 x 103 +1 x 100
35.
(25)6 = 211
36.
Express the following as a product of prime factors:
72
37.
If 2n+2 - 2n+1 +2n = c x 2n, then find the value of c.
38.
Find the value of n, where n is an integer and \({ 2 }^{ n-5 }\times { 6 }^{ 2n-4 }=\frac { 1 }{ { 12 }^{ 4 }\times 2 } \).
39.
If the distance between Earth and Moon is 384000000 m and the distance between the Sun and the Earth is 146900000000 m. Then, which have more distance moon or Sun from Earth. Explain it with the help of standard form of the number.
40.
Simplify \(\frac { { 5 }^{ -2 }\times { 3 }^{ -3 }\times (125)^{ 2/3 } }{ (27)^{ -2/3 }\times (32)^{ -1/5 } } \).
41.
Find x, such that \(\left(1\over5\right)^5\times\left(1\over 5\right)^{19}=\left(1\over 5\right)^{8x}\)
42.
Simplify the following:
(a) (6-1 - 8-1)-1 + (2-1 - 3-1)-1
(b) \({ \left\{ { 6 }^{ -1 }+{ \left( \frac { 3 }{ 2 } \right) }^{ -1 } \right\} }^{ -1 }\)
1.
= (d X d X d X .....10 items) X (d X d X d X ... 20 items)
= d X d X d X ... 30 items
=\({ d }^{ \boxed { 30 } }\)
2.
81
3.
54
4.
(-3)2 \(\div\) p2
\(=({-3\over p})^2\)
5.
\(\frac{3^7}{3^4\times 3^3}\times 9=\frac{3^7}{3^{(3+4)}}\times 9\)
\(=\frac{3^7}{3^7}\times 9=9\)
6.
l5 x m3
7.
Expanded form of 3006194
= 3 x 1000000 + 0 x 100000 + 0 x 10000 + 6x 1000 + 1 x 100 + 9 x 10 + 4 x 1
= 3 x 106 + 0 x 105 + 0 x 104 + 6 x 103 + 1x102 + 9 x 101 + 4 x 100 [\(\because\)100 = 1]
8.
Given, (-3)3 x (-10)3
(- 3)3 = (- 3) x (- 3) x (- 3) = - 27
and (-10)3 = (-10) x (-10) x (-10) = -1000
So, (-3)3 x (-10)3 =(-27) x (-1000)
=27000 =303
9.
210x510
10.
32 x 34 x 38 = (32+4)x38 [\(\because\)am x an =am+n]
=36 x38 =36+8 =314
11.
25 x 27 =25+7 =212 [\(\because\) am x an = am+n]
12.
\(-\frac { 11 }{ 7 } \)
13.
Wehave,0x102 = 0x(10x10)=0x100=0
Hence, the value of 0 x102 is 0.
14.
We have, 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 29 [since, 2 is multiplied 9 times]
Hence, the exponential form of 512 is 29
15.
26 = 2 x 2 x 2 x 2 x 2 x 2 = 64
Hence, the value of 26 is 64
16.
(d)
1 x 1011
17.
30 + 40 + 50 = 1 + 1 + 1 = 3
18.
23 x 24 = 23 +4 = 27
19.
(a)
8
20.
64 = 2 x 2 x 2 x 2 x 2 x 2 = 26
21.
(c)
(x \(\div\) y)5
22.
(a)
(-7)8
23.
(b)
\(\frac { 625 }{ 1296 } \)
24.
(d)
1
25.
(a)
\(\left( \frac { -5 }{ 2 } \right) ^{ 2 }\)
26.
( )
1.496 x 1011
27.
( )
\({1\over3}\)x\({1\over3}\)x\({1\over3}\)x\({1\over3}\)
28.
( )
\(({6\over 7})^2\)
29.
( )
10000 < 105
30.
( )
8.888
31.
( )
\(\left( \frac { 11 }{ 15 } \right) ^{ 5 }\).
32.
(b)
33.
(b)
34.
(a)
35.
(b)
36.
23 x 32
37.
Given, 2n+2- 2n = c x 2n
⇒ 2n+2 = 2n x 22, 2n+1 = 2n x 21
So, 2n x 22 - 2n x 21 + 2n = c x 2n
Taking ~ common from both the side, we get
2n (22-21)= c x 2n
⇒ (22-21+1)c
∴ c = 4-2+1 [∵ 22= 2 x 2=4, 21=2]
=2 +1 =3
38.
Given, \({ 2 }^{ n-5 }\times { 6 }^{ 2n-4 }=\frac { 1 }{ 12^{ 4 }\times 2 } \)
∵ 62n-4 = (2 x 3)2n-4 = 22n-4 x 32n-4
and 124 = (3 x 4)4 =(3 x 2 x 2)4 = 34 x 24 x 24
So, 2n-5 x 22n-4 x 32n-4 =\(\frac { 1 }{ { 3 }^{ 4 }\times { 2 }^{ 4 }\times { 2 }^{ 4 }\times { 2 }^{ 1 } } \)
⇒ 2n-5+2n-4 x 32n-4 =\(\frac { 1 }{ { 3 }^{ 4 }\times { 2 }^{ 4+4+1 } } \)
[∵ am x an =am+n]
⇒ 23n-9 x 32n-4 = \(\frac { 1 }{ { 3 }^{ 4 }\times { 2 }^{ 9 } } \)
⇒ 23n-9 x 32n-4 = 3-4 x 2-9
[∵ a-m=\(\frac { 1 }{ { a }^{ m } } \)]
am =an ⇒ m=n
So,3n-9 = -9
3n = - 9 + 9 = 0 ⇒ n = 0
39.
Distance between Earth and Moon = 384000000 m
=384 x 106
=3.84 x108m ........(i)
and Distance between Sun and Earth = 146900000000
= 1469x108 .......(ii)
Comparing Eqs. (i) and (ii), we see that
3.84 x108 < 1469 x108 [\(\because\) 3.84 < 1469]
So, distance between Sun and Earth is more than distance between Earth and Moon.
40.
\(\frac { { 5 }^{ -2 }\times { 3 }^{ -3 }\times (125)^{ 2/3 } }{ (27)^{ -2/3 }\times (32)^{ -1/5 } } \)
∵ 125 = (5)3 = 5 x 5 x 5
So, (125)2/3 =(5)3 x 2/3 =52 and 27=(3)3
∴ (27)-2/3 = {(3)3}-2/3 =\({ (3 })^{ 3\times \frac { -2 }{ 3 } }\) =(3)2
32 = 2 x 2 x 2 x 2 x 2 = (2)5
So, (32)-1/5 = {(2)5}-1/5 = \({ (2) }^{ 5\times \frac { (-1) }{ 5 } }\)=(2)-1
Now \(\frac { { 5 }^{ -2 }\times { 3 }^{ -3 }\times { 5 }^{ 2 } }{ (3)^{ -2 }\times (2)^{ -1 } } \) \(\left[ \because a^{ -m }=\frac { 1 }{ { a }^{ m } } \right] \)
= 5-2 x 3-3 x 32 x 21 x 52
=5-2+2 x 3-3+2 x 21
am x an =am+n
=50 x 3-1 x 21 = 1 x \(\frac { 1 }{ 3 } \times 2=\frac { 2 }{ 3 } \).
41.
\(⇒\ \left(1\over 5\right)^{5+19}=\left(1\over 5\right)^{8x}\)
[∵ am x an = am+n]
\(⇒\ \left(1\over 5\right)^{24}=\left(1\over 5\right)^{8x}\)
When bases are equal, then by equating their exponents, we get
8x = 24
\(∴\ x={24\over 8}=3\)
42.
(a) (6-1 - 8-1)-1 + (2-1 - 3-1)-1
\(=(\frac{1}{6}-\frac{1}{8})^{-1}+(\frac{1}{2}-\frac{1}{3})^{-1}\)
\(=(\frac{4-3}{24})^{-1}+(\frac{3-2}{6})^{-1}\)
\((\frac{1}{24})^{-1}+(\frac{1}{6})^{-1}\)
= 24 + 6 = 30
(b) \({ \left\{ { 6 }^{ -1 }+{ \left( \frac { 3 }{ 2 } \right) }^{ -1 } \right\} }^{ -1 }\)
\(=(\frac{1}{6}+\frac{2}{3})^{-1}\)
\(=(\frac{1+4}{6})^{-1}=(\frac{5}{6})^{-1}\)
\(=\frac{6}{5}\)
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