Complete step-by-step solutions for DAV Class 7 Secondary Mathematics Chapter 4: Exponents and Powers (Brain Teasers, HOTS & Value Based Questions). Includes all laws of exponents, base comparisons, standard and scientific notations, finding unknown variable x in powers, Higher Order Thinking Skills (HOTS), and Value-Based Questions (VBQs) strictly aligned with the DAV Education Board curriculum.
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Q.1. (A) Tick (✓) the correct option
(i) The exponential form of [((22)2)3] is:
- (a) 45
- (b) 212
- (c) (12)2
- (d) 27
Using the power of a power law: [((am)n)p] = a(m × n × p)
= 2(2 × 2 × 3) = 212.
Correct Option: (b) 212
(ii) 2.7 × 10−3 is equal to:
- (a) 0.000027
- (b) 0.00027
- (c) 0.0027
- (d) 2.007
2.7 × 10−3 = 2.7/103 = 2.7/1000 = 0.0027.
Correct Option: (c) 0.0027
(iii) 9 × 42 is the same as:
- (a) (12)2
- (b) (36)2
- (c) (36)3
- (d) (18)4
9 = 32.
9 × 42 = 32 × 42 = (3 × 4)2 = (12)2.
Correct Option: (a) (12)2
(iv) 10 × 1011 is equal to:
- (a) (100)4
- (b) (10)10
- (c) (100)12
- (d) (10)12
101 × 1011 = 10(1 + 11) = (10)12.
Correct Option: (d) (10)12
(v) If (3/5)2x = 1, then x is equal to:
- (a) 2
- (b) 0
- (c) 1
- (d) 1/2
Since a0 = 1 for any non-zero rational number:
(3/5)2x = (3/5)0
Equating powers: 2x = 0 ⇒ x = 0.
Correct Option: (b) 0
Q.1. (B) Short Answer Questions
(a) Express 108 × 192 as a product of prime factors in exponential form.
• 192 = 26 × 31
108 × 192 = 2(2 + 6) × 3(3 + 1) = 28 × 34.
Ans: 28 × 34
(b) Which is greater: 23 or 32?
Ans: 32
(c) Simplify: (−1)3 × (−1)4 × (−1)5.
Ans: 1
(d) Find the value of (20 + 30) × 40.
Ans: 2
(e) Express 3,43,000 in standard scientific notation.
Ans: 3.43 × 105
Q.2. Simplify and express in exponential form using laws of exponents
(i) Simplify: (23 × 34 × 4)/(3 × 32)
Numerator = 23 × 22 × 34 = 25 × 34.
Denominator = 25 × 31.
Expression = (25 × 34)/(25 × 31) = 2(5 − 5) × 3(4 − 1) = 20 × 33 = 1 × 33 = 33 (or 27).
Ans: 33
(ii) Simplify: ((25)2 × 73)/(83 × 7)
= (210 × 73)/(29 × 71) = 2(10 − 9) × 7(3 − 1) = 21 × 72 = 2 × 49 = 98.
Ans: 2 × 72 = 98
🔥 Higher Order Thinking Skills (HOTS)
HOTS Q1: Find x if 2x − 1 + 2x + 1 = 320.
2x × 2−1 + 2x × 21 = 320
2x × (1/2 + 2) = 320
2x × (5/2) = 320
2x = (320 × 2)/5 = 64 × 2 = 128.
Since 128 = 27, we have 2x = 27 ⇒ x = 7.
Ans: x = 7
HOTS Q2: Simplify: [ (1/3)−2 − (1/2)−3 ] ÷ (1/4)−2.
• (1/3)−2 = 32 = 9
• (1/2)−3 = 23 = 8
• (1/4)−2 = 42 = 16
[ 9 − 8 ] ÷ 16 = 1 ÷ 16 = 1/16.
Ans: 1/16
🌱 Value Based Questions (VBQ)
VBQ: In a science quiz on astrophysics, students learned that the average distance from the Earth to the Sun is approximately 149,600,000 kilometres.
(a) Express this astronomical distance in standard scientific form (m × 10k).
149,600,000 km = 1.496 × 108 km.(b) Why is standard form preferred in science and astronomy? What value does it reflect?
Core Values Depicted: Scientific curiosity, clarity in communication, precision, and humility in contemplating the vastness of the universe.Ans: (a) 1.496 × 108 km | (b) Scientific Temper & Precision
📚 DAV Class 7 Maths Chapter 4: Exponents and Powers – Complete Solutions Index
| Worksheet / Section | Laws of Exponents Covered | Solution Link |
|---|---|---|
| Worksheet 1 | Base, Exponent & Repeated Multiplication | View Worksheet 1 → |
| Worksheet 2 | Product Law (am × an = am+n) | View Worksheet 2 → |
| Worksheet 3 | Quotient Law (am ÷ an = am-n) | View Worksheet 3 → |
| Worksheet 4 | Power of a Power Law ((am)n = amn) | View Worksheet 4 → |
| Worksheet 5 | Zero & Negative Exponents (a0 = 1, a-n) | View Worksheet 5 → |
| Worksheet 6 | Standard Form & Scientific Notation | View Worksheet 6 → |
| Brain Teasers, HOTS & VBQs | Comprehensive Review, Power Equations & Prime Products | Current Page |