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

1.	Identify the greater number, wherever possible in each of the following. (i) 53 or 35(ii) 28 or 82(iii) 1002 or 21000(iv) 210 or 102
Answer» (i) 5³ or 3⁵ 5³ = 5 x 5 x 5 = 125 3⁵ = 3 x 3 x 3 x 3 x 3 = 243 243 > 125 ∴ 3⁵ > 5³ (ii) 2⁸ or 8² 2⁸ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 8² = 8 x 8 = 64 256 > 64 ∴ 2⁸ > 8² (iii) 100² or 2¹⁰⁰⁰ We have 100² = 100 x 100 = 10000 2¹⁰⁰ = (2¹⁰)¹⁰ = (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2)¹⁰ = (1024)¹⁰ = [(1024)²]⁵ = (1024 x 1024)⁵ = (1048576)⁵ Since 1048576 > 10000 (1048576)⁵ > 10000 i.e., (1048576) > 100² (2¹⁰)¹⁰ > 100² 2¹⁰⁰ > 100² (iv) 2¹⁰ or 10² We have 2¹⁰ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024 10² = 10 x 10 = 100 Since 1024 > 100 2¹⁰ > 10²

Identify the greater number, wherever possible in each of the following. (i) 53 or 35(ii) 28 or 82(iii) 1002 or 21000(iv) 210 or 102

Answer»

(i) 5³ or 3⁵ 5³ = 5 x 5 x 5

= 125

3⁵ = 3 x 3 x 3 x 3 x 3

= 243

243 > 125

∴ 3⁵ > 5³

(ii) 2⁸ or 8²

2⁸ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 256

8² = 8 x 8

= 64

256 > 64

∴ 2⁸ > 8²

(iii) 100² or 2¹⁰⁰⁰

We have 100² = 100 x 100

= 10000

2¹⁰⁰ = (2¹⁰)¹⁰

= (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2)¹⁰

= (1024)¹⁰

= [(1024)²]⁵

= (1024 x 1024)⁵

= (1048576)⁵

Since 1048576 > 10000

(1048576)⁵ > 10000

i.e., (1048576) > 100²

(2¹⁰)¹⁰ > 100²

2¹⁰⁰ > 100²

(iv) 2¹⁰ or 10²

We have 2¹⁰ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 1024

10² = 10 x 10

= 100

Since 1024 > 100

2¹⁰ > 10²