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By Maitree Choube
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Updated on 18 Oct 2025, 11:56 IST
Chapter 13 Exponents and Powers Class 7 is a bit tricky and most students find it Difficult because of its calculation. Exponents and Power helps to understand how to write very large or very small numbers in a short and easy way using exponents.
Practicing MCQ Questions for Class 7 Maths Chapter 13 Exponents and Powers really help in building concepts and improve problem-solving speed. These multiple-choice questions cover all important topics like laws of exponents, powers of numbers, and standard form, making it easier to revise quickly. If students practice these MCQ questions for class 7 Maths regularly they will surely get a good command on this topic and will able to score more marks in their exams
These questions are made according to NCERT Solutions for Class 7 Maths and follow the CBSE pattern.
An exponent shows how many times a number (called the base) is multiplied by itself. It is a short way to express repeated multiplication.
Example: (3)^4 = 3×3×3×3=81
Here, 3 is the base and 4 is the exponent (or power). It means 3 is multiplied by itself 4 times.
Exponents and Powers write big or repeated numbers in a smaller, smarter, and more convenient way.
Also Check:
| Product Law | No. | Law of Exponent | Rule / Formula | |
| 1 | Product Law | am × an = am+n | 23 × 24 = 27 = 128 | When bases are same, add exponents. |
| 2 | Quotient Law | am ÷ an = am−n | 56 ÷ 52 = 54 = 625 | When dividing same bases, subtract exponents. |
| 3 | Power of a Power | (am)n = am×n | (32)3 = 36 = 729 | Multiply exponents when a power has another power. |
| 4 | Power of a Product | (ab)m = am × bm | (2×3)2 = 22 × 32 = 4×9 = 36 | Distribute the exponent to both numbers inside brackets. |
| 5 | Power of a Quotient | (a/b)m = am / bm | (4/2)3 = 43/23 = 64/8 = 8 | Apply the exponent to both numerator and denominator. |
| 6 | Zero Exponent Law | a0 = 1 (for a ≠ 0) | 90 = 1 | Any non-zero number raised to zero is always 1. |
| 7 | Negative Exponent Law | a−m = 1 / am | 2−3 = 1 / 23 = 1/8 | Negative exponent means reciprocal of the number. |
| 8 | Exponent of 1 Law | a1 = a | 71 = 7 | Any number raised to power 1 stays the same. |
| 9 | Same Power Law | am × bm = (ab)m | 23 × 33 = (2×3)3 = 63 = 216 | When exponents are same, multiply the bases. |
| 10 | Division with Same Power Law | am / bm = (a/b)m | 42 / 22 = (4/2)2 = 22 = 4 | When exponents are same, divide the bases. |
| 11 | Exponent of Zero Base | 0m = 0 (for m > 0) | 05 = 0 | Zero raised to any positive power is always zero. |
1. The value of 2³ × 2⁴ is:
A) 14
B) 16
C) 128
D) 256
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Correct Answer: C) 128
2. 5⁴ ÷ 5² = ?
A) 5²
B) 5⁶
C) 5¹
D) 5⁰
Correct Answer: A) 5²
3. The reciprocal of 3⁻⁴ is:
A) 3⁴
B) 3⁻⁸
C) 1/3⁴
D) 3⁻¹ A) 3⁴
4. Simplify (2³)²
A) 2⁵
B) 2⁶
C) 2⁸
D) 2⁹
Correct Answer: B) 2⁶
5. Which of the following is equal to 10⁻³?
A) 0.003
B) 0.03
C) 0.0003
D) 0.3
Correct Answer: C) 0.0003
6. (7⁰ + 8⁰) × 9⁰ = ?
A) 1
B) 2
C) 3
D) 0
Correct Answer: C) 3
7. The standard form of 0.00045 is:
A) 4.5×10⁻³
B) 4.5×10⁻⁴
C) 45×10⁻⁴
D) 0.45×10⁻³
Correct Answer: B) 4.5×10⁻⁴
8. Simplify 8⁵ ÷ 8³
A) 8²
B) 8⁸
C) 8⁵
D) 8⁰
Correct Answer: A) 8²
9. 4⁻² = ?
A) 1/4²
B) 4²
C) 1
D) 1/8
Correct Answer: A) 1/4²
10. Which expression equals (3² × 3³)?
A) 3⁵
B) 3⁶
C) 3¹
D) 3¹⁰
Correct Answer: A) 3⁵
11. Simplify (5³)⁰
A) 0
B) 1
C) 5
D) 5³
Correct Answer: B) 1
12. (2×5)³ = ?
A) 10³
B) 7³
C) 2³ + 5³
D) 2³ × 5²
Correct Answer: A) 10³
13. Which of the following is true?
A) aᵐ + aⁿ = aᵐ⁺ⁿ
B) aᵐ × aⁿ = aᵐ⁺ⁿ
C) aᵐ − aⁿ = aᵐ⁻ⁿ
D) aᵐ/aⁿ = aᵐ×ⁿ
Correct Answer: B) aᵐ × aⁿ = aᵐ⁺ⁿ
14. Simplify (9²)1/2
A) 3
B) 9
C) 81
D) 18
Correct Answer: (B) 9
15. (x⁴ × x⁻²) = ?
A) x⁶
B) x²
C) x⁻⁸
D) x⁰
Correct Answer: B) x²
16. The value of 6¹ × 6⁻¹ is:
A) 0
B) 6
C) 1
D) 6⁻²
Correct Answer: C) 1
17. The exponential form of 625 is:
A) 5²
B) 5³
C) 5⁴
D) 5⁵
Correct Answer: C) 5⁴
18. The value of (−2)³ is:
A) −8
B) 8
C) 4
D) −6
Correct Answer: A) −8
19. Simplify (a²b³)²
A) a⁴b⁶
B) a³b²
C) a²b³
D) a⁵b⁵
Correct Answer: A) a⁴b⁶
20. (x⁻³)⁻² = ?
A) x⁻⁶
B) x⁶
C) x⁻¹.⁵
D) x⁰
Correct Answer: B) x⁶
21. 1000 = 10ⁿ. What is n?
A) 1
B) 2
C) 3
D) 4
Correct Answer: C) 3
22. Simplify 9⁻¹ × 9³
A) 9²
B) 9⁻⁴
C) 9¹
D) 9⁰
Correct Answer: A) 9²
23. 2¹⁰ ÷ 2⁵ = ?
A) 2²
B) 2³
C) 2⁵
D) 2¹⁵
Correct Answer: C) 2⁵
24. The standard form of 7200000 is:
A) 7.2×10⁶
B) 7.2×10⁵
C) 72×10⁵
D) 0.72×10⁸
Correct Answer: A) 7.2×10⁶
25. Simplify (3² × 2²)²
A) 6⁴
B) 36²
C) 3⁴ × 2⁴
D) All of these
Correct Answer: D) All of these
26. 10⁰ + 2⁰ = ?
A) 0
B) 1
C) 2
D) 3
Correct Answer: C) 2
27. a⁻³ × a⁵ = ?
A) a⁸
B) a⁻⁸
C) a²
D) a⁰
Correct Answer: C) a²
28. If 2ˣ = 8, then x = ?
A) 2
B) 3
C) 4
D) 5
Correct Answer: B) 3
29. Simplify (4³ ÷ 4²) × 4¹
A) 4⁰
B) 4²
C) 4³
D) 4⁴
Correct Answer: C) 4³
30. (ab)⁻¹ = ?
A) a⁻¹b⁻¹
B) ab
C) (a+b)⁻¹
D) a⁻¹/b
Correct Answer: A) a⁻¹b⁻¹
31. The value of 5³ − 5⁰ is:
A) 125
B) 124
C) 126
D) 0
Correct Answer: B) 124
32. Simplify (2⁻²)³
A) 2⁻⁵
B) 2⁻⁶
C) 2⁵
D) 2⁶
Correct Answer: B) 2⁻⁶
33. 7ˣ = 49. What is x?
A) 1
B) 2
C) 3
D) 4
Correct Answer: B) 2
34. Simplify (5² × 5⁻³) ÷ 5⁻¹
A) 5⁰
B) 5²
C) 5³
D) 5⁻²
Correct Answer: B) 5²
35. Which of the following is in exponential form?
A) 2×2×2×2
B) 2⁴
C) 2+4
D) 2÷4
Correct Answer: B) 2⁴
1. A bacteria doubles every hour. If one bacteria is present initially, how many will be there after 5 hours?
Answer: 2⁵ = 32 bacteria
When something doubles repeatedly, we use powers of 2.
2. The side of a cube is 2³ cm. Find its volume.
Answer: (2³)³ = 2⁹ = 512 cm³
Cube of a cube → multiply exponents (3 × 3).
3. A laptop’s power reduces to one-fourth every hour. If its initial power is 100%, what remains after 2 hours?
Answer: (1/4)² = 1/16 = 6.25%
Repeated reduction uses powers of a fraction.
4. If 3ˣ = 81, find x.
Answer: 81 = 3⁴ ⇒ x = 4
Write both sides with the same base and compare powers.
5. A ball bounces to half its height each time. If the first height is 16 m, what height after 3 bounces?
Answer: 16 × (1/2)³ = 2 m
Successive halves → power of ½.
6. Simplify: (5² × 5³) ÷ 5⁴
Answer: 5²⁺³⁻⁴ = 5¹ = 5
Use laws of exponents: aᵐ × aⁿ = aᵐ⁺ⁿ
7. Cells multiply 8 times in 4 hours. Express using exponents.
Answer: (2³)⁴ = 2¹² cells
Repeating pattern → use power of a power.
8. Simplify: (2³ × 3²)²
Answer: 2⁶ × 3⁴
Multiply exponents inside parentheses.
9. A town’s population is 2⁵. It doubles every year. Population after 3 years?
Answer: 2⁵ × 2³ = 2⁸ = 256
Doubling → multiply by powers of 2.
10. Express 0.0000025 in standard form.
Answer: 2.5 × 10⁻⁶
Move decimal after first non-zero digit and count places.
11. Simplify: 3⁴ × 3⁻² ÷ 3³
Answer: 3⁻¹ = 1/3
Use exponent rules when dividing powers.
12. Find the value: (10⁻²)³ × 10⁵
Answer: 10⁻⁶ × 10⁵ = 10⁻¹ = 0.1
Add exponents for same base multiplication.
13. Simplify: (4⁻¹ × 2²)²
Answer: (1/4 × 4)² = 1² = 1
Negative exponent means reciprocal.
14. If 5ˣ⁺¹ = 125, find x.
Answer: 125 = 5³ ⇒ x + 1 = 3 ⇒ x = 2
Make the base same and equate powers.
15. A grain of rice doubles every second. How many grains after 10 seconds starting from 1?
Answer: 2¹⁰ = 1024 grains
Also Check:
| S.No. | Subject |
| 1 | NCERT Solutions for Class 7 Maths |
| 2 | NCERT Solutions for Class 7 Science |
| 3 | NCERT Solutions for Class 7 Social Science |
| 4 | NCERT Solutions for Class 7 English |
| 5 | NCERT Solutions for Class 7 Hindi |
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Yes Both refers to same term that show how many times a number (base) is multiplied by itself. Example: 3^3 = 3 × 3 × 3 = 27
To solve MCQs, remember the laws of exponents:
1. Add powers when multiplying same bases:
am × an = am+n
2. Subtract powers when dividing same bases:
am ÷ an = am−n
3. Multiply powers when raising a power to another power:
(am)n = am×n
Power of 2 means multiplying 2 by itself repeatedly:
21 = 2,
22 = 4,
23 = 8,
24 = 16,
25 = 32
21 = 2,
22 = 4,
23 = 8,
24 = 16,
25 = 32,
26 = 64,
27 = 128
Practice free Class 7 Exponents and Powers MCQs on Infinity learn website that provide instant answers, timed tests, and chapter-wise MCQs.