Question

Identify the greater 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 1

(i) 4³ = 4 × 4 × 4 = 64

3⁴ = 3 × 3 × 3 × 3 = 81

Therefore, 3⁴ > 4³

(ii) 5³ = 5 × 5 × 5 =125

3⁵ = 3 × 3 × 3 × 3 × 3 = 243

Therefore, 3⁵ > 5³

(iii) 2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

8² = 8 × 8 = 64

Therefore, 2⁸ > 8²

(iv)100² or 2¹⁰⁰

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

2¹⁰⁰ = 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 ×1024 × 1024

100² = 100 × 100 = 10000

Therefore, 2¹⁰⁰ > 100²

(v) 2¹⁰ and 10²

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

10² = 10 × 10 = 100

Therefore, 2¹⁰ > 10²