Question

Arrange in ascending order:

2⁵, 3³, 2³ × 2, (3³)², 3⁵, 4⁰, 2³ × 3¹

Answer 1

In ascending order, the numbers are arranged from smallest to largest.

We have, 2⁵ = 2 × 2 × 2 × 2 × 2 = 32

3³ = 3 × 3 × 3 = 27

2³ × 2 = 2 × 2 × 2 × 2 = 16

(3³)² = 3^{3 × 2}   ...[∴ (a^m)ⁿ = a^mn]

3⁶ = 3 × 3 × 3 × 3 × 3 × 3 = 729

3⁵ = 3 × 3 × 3 × 3 × 3 = 243

4° = 1  ...[∴ a⁰ = 1]

And 2³ × 3¹ = 2 × 2 × 2 × 3 = 24

Thus, the required ascending order will be 4° < 2³ × 2 < 23 × 31 < 33 < 25 < 35 < (33)².