CHAPTER – 13 Exponents and Powers | CLASS 7TH |NCERT MATHS IMPORTANT QUESTIONS & MCQS

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MATHS IMPORTANT QUESTIONS & MCQS FOR CLASS 7th

Get Chapter Wise MCQ Questions for Class 7 Maths with Answers prepared here according to the latest CBSE syllabus and NCERT curriculum. Students can practice CBSE Class 7 Maths MCQs Multiple Choice Questions with Answers to score good marks in the examination. Students can also visit the most accurate and elaborate NCERT Solutions for Class 7 Maths. Every question of the textbook has been answered here.

Chapter - 13 Exponents and Powers

MCQs

Question 1.
The exponential form of 10000 is
(a) 10³
(b) 10⁴
(c) 10⁵
(d) none of these

Answer

Answer: (b) 10⁴
Hint:
10000 = 10 × 10 × 10 × 10 = 10⁴

Question 2.
The exponential form of 100000 is
(a) 10³
(b) 10⁴
(c) 10⁵
(d) none of these

Answer

Answer: (c) 10⁵
Hint:
100000 = 10 × 10 × 10 × 10 × 10 = 10⁵

Question 3.
The exponential form of 81 is
(a) 3⁴
(b) 3³
(c) 3²
(d) none of these

Answer

Answer: (a) 3⁴
Hint:
81 = 3 × 3 × 3 × 3 = 3⁴

Question 4.
The exponential form of 125 is
(a) 5⁴
(b) 5³
(c) 5²
(d) none of these

Answer

Answer: (b) 5³
Hint:
125 = 5 × 5 × 5 = 5³

Question 5.
The exponential form of 32 is
(a) 2³
(b) 2⁴
(c) 2⁵
(d) none of these

Answer

Answer: (c) 2⁵
Hint:
32 = 2 × 2 × 2 × 2 × 2 = 2⁵

Question 6.
The exponential form of 243 is
(a) 3⁵
(b) 3⁴
(c) 3³
(d) 3²

Answer

Answer: (a) 3⁵
Hint:
243 = 3 × 3 × 3 × 3 × 3 = 3⁵

Question 7.
The exponential form of 64 is
(a) 2⁵
(b) 2⁶
(c) 2⁷
(d) 2⁸

Answer

Answer: (b) 2⁶
Hint:
64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

Question 8.
The exponential form of 625 is
(a) 5²
(b) 5³
(c) 5⁴
(d) 5⁵

Answer

Answer: (c) 5⁴
Hint:
625 = 5 × 5 × 5 × 5 = 5⁴

Question 9.
The exponential form of 1000 is
(a) 10¹
(b) 10²
(c) 10³
(d) 10⁴

Answer

Answer: (c) 10³
Hint:
1000 = 10 × 10 × 10 = 10³

Question 10.
The value of (- 2)³ is
(a) 8
(b) -8
(c) 16
(d) -16

Answer

Answer: (b) -8
Hint:
(-2)³ = (-2) × (-2) × (-2) = -8

Question 11.
The value of (- 2)⁴ is
(a) 8
(b) -8
(c) 16
(d) -16

Answer

Answer: (c) 16
Hint:
(-2)⁴ = (-2) × (-2) × (-2) × (-2) = 16

Question 12.
What is the base in 8²?
(a) 8
(b) 2
(c) 6
(d) 10

Answer

Answer: (a) 8

Question 13.
What is the exponent in 8²?
(a) 8
(b) 2
(c) 16
(d) 6

Answer

Answer: (b) 2

Question 14.
(-1)^{even number} =
(a) -1
(b) 1
(c) 0
(d) none of these

Answer

Answer: (b) 1

Question 15.
(-1)^{odd number} =
(a) -1
(b) 1
(c) 0
(d) none of these

Answer

Answer: (a) -1

Question 16.
0 × 10⁴ =
(a) 0
(b) 10⁴
(c) 1
(d) none of these

Answer

Answer: (a) 0

Question 17.
If 2³ × 2⁴ = 2^?, then ? =
(a) 3
(b) 4
(c) 1
(d) 7

Answer

Answer: (d) 7
Hint:
2³ × 2⁴ = 2³⁺⁴ = 2⁷

Important Questions

Question 1.
Express 343 as a power of 7.
Solution:
We have 343 = 7 × 7 × 7 = 7³
Thus, 343 = 7³

Question 2.
Which is greater 3² or 2³?
Solution:
We have 3² = 3 × 3 = 9
2³ = 2 × 2 × 2 = 8
Since 9 > 8
Thus, 3² > 2³

Question 3.
Express the following number as a powers of prime factors:
(i) 144
(ii) 225
Solution:
(i) We have
144 = 2 × 2 × 2 × 2 × 3 × 3 = 2⁴ × 3²
Thus, 144 = 2⁴ × 3²

(ii) We have
225 = 3 × 3 × 5 × 5 = 3² × 5²
Thus, 225 = 3² × 5²

Question 4.
Find the value of:
(i) (-1)¹⁰⁰⁰
(ii) (1)²⁵⁰
(iii) (-1)¹²¹
(iv) (10000)⁰
Solution:
(i) (-1)¹⁰⁰⁰ = 1 [∵ (-1)^{even number} = 1]
(ii) (1)²⁵⁰ = 1 [∵ (1)^{even number} = 1]
(iii) (-1)¹²¹ = -1 [∵ (-1)^{odd number} = -1]
(iv) (10000)⁰ = 1 [∵ a⁰ = 1]

Question 5.
Express the following in exponential form:
(i) 5 × 5 × 5 × 5 × 5
(ii) 4 × 4 × 4 × 5 × 5 × 5
(iii) (-1) × (-1) × (-1) × (-1) × (-1)
(iv) a × a × a × b × c × c × c × d × d
Solution:
(i) 5 × 5 × 5 × 5 × 5 = (5)⁵
(ii) 4 × 4 × 4 × 5 × 5 × 5 = 4³ × 5³
(iii) (-1) × (-1) × (-1) × (-1) × (-1) = (-1)⁵
(iv) a × a × a × b × c × c × c × d × d = a³b¹c³d²

Question 6.
Express each of the following as product of powers of their prime factors:
(i) 405
(ii) 504
(iii) 500
Solution:
(i) We have
405 = 3 × 3 × 3 × 3 × 5 = 3⁴ × 5¹
Thus, 405 = 3⁴ × 5¹

(ii) We have
504 = 2 × 2 × 2 × 3 × 3 × 7 = 2³ × 3² × 7¹
Thus, 504 = 2³ × 3² × 7¹

(iii) We have
500 = 2 × 2 × 5 × 5 × 5 = 2² × 5³
Thus, 500 = 2² × 5³

Question 7.
Simplify the following and write in exponential form:
(i) (5²)³
(ii) (2³)³
(iii) (a^b)^c
(iv) [(5)²]²
Solution:
(i) (5²)³ = 5^2×3 = 5⁶
(ii) (2³)³ = 2^3×3 = 2⁹
(iii) (a^b)^c = a^b×c = a^bc
(iv) [(5)²]² = 5^2×2 = 5⁴

Question 8.
Verify the following:

Solution:

Question 9.
Simplify:

Solution:

Question 10.
Simplify and write in exponential form:

Solution:

Exponents and Powers Class 7 Extra Questions Short Answer Type

Question 11.
Express each of the following as a product of prime factors is the exponential form:
(i) 729 × 125
(ii) 384 × 147
Solution:
(i) 729 × 125 = 3 × 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5 = 3⁶ × 5³
Thus, 729 × 125 = 3⁶ × 5³

(ii) 384 × 147 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7 = 2⁷ × 3² × 7²
Thus, 384 × 147 = 2⁷ × 3² × 7²

Question 12.
Simplify the following:
(i) 10³ × 9⁰ + 3³ × 2 + 7⁰
(ii) 6³ × 7⁰ + (-3)⁴ – 9⁰
Solution:
(i) 10³ × 9⁰ + 3³ × 2 + 7⁰
= 1000 + 54 + 1
= 1055
(ii) 6³ × 7⁰ + (-3)⁴ – 9⁰
= 216 × 1 + 81 – 1
= 216 + 80
= 296

Question 13.
Write the following in expanded form:
(i) 70,824
(ii) 1,69,835
Solution:
(i) 70,824
= 7 × 10000 + 0 × 1000 + 8 × 100 + 2 × 10 + 4 × 10⁰
= 7 × 10⁴ + 8 × 10² + 2 × 10¹ + 4 × 10⁰
(ii) 1,69,835
= 1 × 100000 + 6 × 10000 + 9 × 1000 + 8 × 100 + 3 × 10 + 5 × 10⁰
= 1 × 10⁵ + 6 × 10⁴ + 9 × 10³ + 8 × 10² + 3 × 10¹ + 5 × 10⁰

Question 14.
Find the number from each of the expanded form:
(i) 7 × 10⁸ + 3 × 10⁵ + 7 × 10² + 6 × 10¹ + 9
(ii) 4 × 10⁷ + 6 × 10³ + 5
Solution:
(i) 7 × 10⁸ + 3 × 10⁵ + 7 × 10² + 6 × 10¹ + 9
= 7 × 100000000 + 3 × 100000 + 7 × 100 + 6 × 10 + 9
= 700000000 + 300000 + 700 + 60 + 9
= 700300769
(ii) 4 × 10⁷ + 6 × 10³ + 5
= 4 × 10000000 + 6 × 1000 + 5
= 40000000 + 6000 + 5
= 40006005

Question 15.
Find the value of k in each of the following:

Solution:

Question 16.
Find the value of
(a) 3⁰ ÷ 4⁰
(b) (8⁰ – 2⁰) ÷ (8⁰ + 2⁰)
(c) (2⁰ + 3⁰ + 4⁰) – (4⁰ – 3⁰ – 2⁰)
Solution:
(a) We have 3⁰ ÷ 4⁰ = 1 ÷ 1 = 1 [∵ a⁰ = 1]
(6) (8⁰ – 2⁰) ÷ (8⁰ + 2⁰) = (1 – 1) ÷ (1 + 1) = 0 ÷ 2 = 0
(c) (2⁰ + 3⁰ + 4⁰) – (4⁰ – 3⁰ – 2⁰)
= (1 + 1 + 1) – (1 – 1 – 1) [∵ a⁰ = 1]
= 3 – 1
= 2

Question 17.
Express the following in standard form:
(i) 8,19,00,000
(ii) 5,94,00,00,00,000
(iii) 6892.25
Solution:
(i) 8,19,00,000 = 8.19 × 10⁷
(ii) 5,94,00,00,00,000 = 5.94 × 10¹¹
(iii) 6892.25 = 6.89225 × 10³

Question 18.
Evaluate:

Solution: