Question

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 1

(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