Identify the grater number, wherever possible, in each of the followin

1.	Identify the grater number, wherever possible, in each of the following ?(i) 43 or 34(ii) 53 or 35(iii) 28 or 82(iv) 1002 or 2100(v) 210 or 102
Answer» (i) 4³ or 3⁴ 4³ = 4 × 4 × 4 = 64 3⁴ = 3 × 3 × 3 × 3 = 81 ∴ 3⁴ > 4³ (ii) 5³ or 3⁵ 5³ = 5 × 5 × 5 = 125 3⁵ = 3 × 3 × 3 × 3 × 3 = 243 ∴ 3⁵ >5³ (iii) 2⁸ or 8² 2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256 8² = 8 × 8 = 64 ∴ 2⁸ > 8² (iv) 100² or 2¹⁰⁰ 100² = 100 × 100= 10,000 2⁸ = (2¹⁰)¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = (1024)¹⁰ = [(1024)²]⁵ = [10,48,576] = (10,48,476)⁵ > 10,000 = 2¹⁰⁰ > 100² (v) 2¹⁰ or 10² 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024 10² = 10 × 10 = 100 ∴ 2¹⁰ > 10²

Identify the grater number, wherever possible, in each of the following ?(i) 43 or 34(ii) 53 or 35(iii) 28 or 82(iv) 1002 or 2100(v) 210 or 102

Answer»

(i) 4³ or 3⁴

4³ = 4 × 4 × 4 = 64

3⁴ = 3 × 3 × 3 × 3 = 81

∴ 3⁴ > 4³

(ii) 5³ or 3⁵

5³ = 5 × 5 × 5 = 125

3⁵ = 3 × 3 × 3 × 3 × 3 = 243

∴ 3⁵ >5³

(iii) 2⁸ or 8²

2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

8² = 8 × 8 = 64

∴ 2⁸ > 8²

(iv) 100² or 2¹⁰⁰

100² = 100 × 100= 10,000

2⁸ = (2¹⁰)¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
× 2 × 2

= (1024)¹⁰ = [(1024)²]⁵ = [10,48,576]

= (10,48,476)⁵ > 10,000

= 2¹⁰⁰ > 100²

(v) 2¹⁰ or 10²

2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

10² = 10 × 10 = 100

∴ 2¹⁰ > 10²