.jpg "Maths 8 Chapter-2 Figure it Out (Page 22–23) Solutions")
NCERT Class 8 Maths Chapter 2 – Figure it Out (Page 22–23) | Exponential Form Solutions
.jpg "Maths 8 Chapter-2 Figure it Out (Page 22–23) Solutions")
Figure it Out
1. Express the following in exponential form:
(i) 6 × 6 × 6 × 6
(ii) y × y (iii) b × b × b × b
(iv) 5 × 5 × 7 × 7 × 7
(v) 2 × 2 × a × a
(vi) a × a × a × c × c × c × c × d
SOLUTIONS:
(i) 6 × 6 × 6 × 6
👉 The number 6 is multiplied 4 times.
✅ Exponential form: 6⁴
(ii) y × y
👉 The variable y is multiplied 2 times.
✅ Exponential form: y²
(iii) b × b × b × b
👉 The variable b is multiplied 4 times.
✅ Exponential form: b⁴
(iv) 5 × 5 × 7 × 7 × 7
👉 The number 5 appears 2 times, and 7 appears 3 times.
✅ Exponential form: 5² × 7³
(v) 2 × 2 × a × a
👉 The number 2 appears 2 times, and a appears 2 times.
✅ Exponential form: 2² × a²
(vi) a × a × a × c × c × c × c × d
👉 The variable a appears 3 times, c appears 4 times, and d appears once.
✅ Exponential form: a³ × c⁴ × d
Final Answers Summary:
(i) 6⁴(ii) y²
(iii) b⁴
(iv) 5² × 7³
(v) 2² × a²
(vi) a³ × c⁴ × d
2. Express each of the following as a product of powers of their prime factors in exponential form.
(i) 648 (ii) 405 (iii) 540 (iv) 3600
SOLUTIONS:
Method (brief)
Keep dividing by the smallest possible prime (2, 3, 5, ...) until you reach 1. Count how many times each prime divides the number — those counts are the exponents.
(i) 648
648 ÷ 2 = 324 → one factor 2
324 ÷ 2 = 162 → second factor 2
162 ÷ 2 = 81 → third factor 2
81 ÷ 3 = 27 → one factor 3
27 ÷ 3 = 9 → second factor 3
9 ÷ 3 = 3 → third factor 3
3 ÷ 3 = 1 → fourth factor 3
So prime factors: three 2’s and four 3’s.
Exponential form: 648 = 2³ × 3⁴
(Check: 2³=8, 3⁴=81 → 8×81 = 648)
(ii) 405
405 ÷ 3 = 135 → one factor 3
135 ÷ 3 = 45 → second factor 3
45 ÷ 3 = 15 → third factor 3
15 ÷ 3 = 5 → fourth factor 3
5 ÷ 5 = 1 → one factor 5
So prime factors: 3⁴ and 5¹.
Exponential form: 405 = 3⁴ × 5
(iii) 540
540 ÷ 2 = 270 → one factor 2
270 ÷ 2 = 135 → second factor 2
135 ÷ 3 = 45 → one factor 3
45 ÷ 3 = 15 → second factor 3
15 ÷ 3 = 5 → third factor 3
5 ÷ 5 = 1 → one factor 5
So prime factors: 2², 3³, 5¹.
Exponential form: 540 = 2² × 3³ × 5
(iv) 3600
You can do this by inspection: 3600 = 36 × 100.
36 = 2² × 3²
100 = 2² × 5²
Multiply powers of same primes: 2² × 2² = 2⁴. So:
Exponential form: 3600 = 2⁴ × 3² × 5²
(Check: 2⁴=16, 3²=9, 5²=25 → 16×9×25 = 16×225 = 3600)
Final Answers Summary:
(i) 648 = 2³ × 3⁴
(ii) 405 = 3⁴ × 5
(iii) 540 = 2² × 3³ × 5
(iv) 3600 = 2⁴ × 3² × 5²
Question: 3. Write the numerical value of each of the following:
(i) 2 × 10³ (ii) 7² × 2³ (iii) 3 × 4⁴
(iv) (– 3)² × (– 5)² (v) 3² × 10⁴ (vi) (– 2)⁵ × (– 10)⁶
Solution: 3 – Numerical value of each of the following
(i) 2 × 10³
10³ = 10 × 10 × 10 = 1000
⇒ 2 × 1000 = 2000
⇒ 2 × 1000 = 2000
(ii) 7² × 2³
7² = 49
2³ = 8
⇒ 49 × 8 = 392
2³ = 8
⇒ 49 × 8 = 392
(iii) 3 × 4⁴
4⁴ = 4 × 4 × 4 × 4 = 256
⇒ 3 × 256 = 768
⇒ 3 × 256 = 768
(iv) (–3)² × (–5)²
(–3)² = 9 (because a negative number raised to an even power becomes positive)
(–5)² = 25
⇒ 9 × 25 = 225
(–5)² = 25
⇒ 9 × 25 = 225
(v) 3² × 10⁴
3² = 9
10⁴ = 10 × 10 × 10 × 10 = 10,000
⇒ 9 × 10,000 = 90,000
(vi) (–2)⁵ × (–10)⁶
(–2)⁵ = –32 (odd power → negative result)
(–10)⁶ = 1,000,000 (even power → positive result)
⇒ (–32) × 1,000,000 = –32,000,000
Final Answers Summary:
Continue Your Grade 8 Maths Journey!
Congratulations on working through these challenging problems! These exercises build a strong foundation for understanding exponents and roots. If you are ready to move on, check out the next section of your curriculum.
.jpg&description=NCERT Class 8 Maths Chapter 2 – Figure it Out (Page 22–23) | Exponential Form Solutions){kind=link}
0 Comments