Question - 2 : -
Exress the following in exponential form:
(i) 6 × 6 × 6 × 6
(ii) t × t
(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

Answer - 2 : -

(i) 6 × 6 × 6 × 6 = 6³
(ii) t × t = t²
(iii) b × b × b × b = b⁴
(iv) 5 × 5× 7 × 7 × 7 = 5² × 7³ = 5² ·7³
(v) 2 × 2 × a × a = 2² × a² = 2² ·a²
(vi) a × a ×a × c × c × c × c × d = a³ ×c⁴ × d = a³ ·c⁴ · d

Question - 3 : -
Express each of the following numbers using exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125

Answer - 3 : -

Question - 4 : - Identify the greater number, wherever possible, ineach of the following?
(i) 4³ or 3⁴
(ii) 5³ or 3⁵
(iii) 2⁸ or 8²
(iv) 100² or 2¹⁰⁰
(v) 2¹⁰ or 10²

Answer - 4 : -

(i) 4³ or 3⁴
4³ = 4 × 4 × 4 = 64,
3⁴ = 3 × 3 × 3 × 3 = 81
Since 81 > 64
∴ 34 isgreater than 43.

(ii) 5³ or 3⁵
5³ = 5 × 5 × 5 = 125
3⁵ = 3 × 3 × 3 × 3 × 3 = 243
Since 243 > 125
∴ 35 isgreater than 53.

(iii) 2⁸ or 8²
2⁸ =2 × 2 × 2 × 2 × 2 × 2 × 2 ×2 = 256
8² = 8 × 8 = 64
Since 256 > 64
∴ 28 isgreater than 28.

(iv) 100² or 2¹⁰⁰
100² = 100 × 100 = 10000
2¹⁰⁰ = 2 × 2 × 2 × … 100 times
Here 2 × 2 × 2 ×2 × 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 × 2 = 214 = 16384
Since 16384 > 10,000
∴ 2100is greater than 1002.

(v) 2¹⁰ or 10²
2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2× 2 × 2 × 2 = 1024
10² = 10 × 10 = 100
Since 1024 > 100
∴ 210 isgreater than 102.

Question - 5 : -
Express each of the following as the product of powers of their prime
(i) 648
(ii) 405
(iii) 540
(iv) 3600

Answer - 5 : -

Question - 6 : - Simplify:
(i) 2 × 10³
(ii) 7² × 2²
(iii) 2³ × 5
(iv) 3 × 4⁴
(v) 0 × 10²
(vi) 5² × 3³
(vii) 2⁴ × 3²
(viii) 3² × 10⁴

Answer - 6 : -

(i) 2 × 10³ = 2 ×10 × 10 × 10 = = 2000
(ii) 7² × 2² = = 7 × 7 × 2 × 2 = 196
(iii) 2³ × 5 = 2 × 2 × 2 × 5 = 40
(iv) 3 × 4⁴ = 3 × 4 × 4 × 4 × 4= 768
(v) 0 × 10² = 0 × 10 × 10 = = 0
(vi) 5² × 3³ = 5 × 5 × 3 × 3 × 3 = 675
(vii) 2⁴ × 3² = 2 × 2 × 2 × 2 × 3 × 3 = 144
(viii) 3² × 10⁴ = 3 × 3 × 10 × 10 × 10 × 10 = 90000

Question - 7 : - Simplify:
(i) (-4)³
(ii) (-3) × (-2)³
(iii) (-3)² × (-5)²
(iv) (-2)³ × (-10)³

Answer - 7 : -

(i) (-4)² = (-4)× (-4) × (-4) = -64 [∵ (-a)^{odd number} = -a^oddnumber]
(ii) (-3) × (-2)³ = (-3) × (-2)× (-2) × (-2)
= (-3) × (-8) = 24
(iii) (-3)² × (-5)² = [(-3) × (-5)]²
= 15² = 225 [∵ a^m ×b^m = (ab)^m)
(iv) (-2)³ × (-10)³ = [(-2) × (-10)]³
= 20² = 8000 [∵ a^m ×b^m = (ab)^m]

Question - 8 : - Compare the following:
(i) 2.7 × 10¹²; 1.5 × 10⁸
(ii) 4 × 10¹⁴; 3 × 10¹⁴

Answer - 8 : -

(i) 2.7 × 10¹²; 1.5 ×10⁸
Here, 10¹² > 10⁸
∴ 2.7 ×10¹²> 1.5 × 10⁸
(ii) 4 × 10¹⁴; 3 × 10¹⁷
Here, 10¹⁷ > 10¹⁴
∴ 4 × 10¹⁴ < 3 × 10¹⁷

Free - Previous Years Question Papers

Chapter 13 Exponents and Powers Ex 13.1 Solutions

Subscribe Now!