I would like to compare two expressions

Question

2 X (5/4)⁴ and 10 X (3/8)³

I know that the first expression is bigger but i don't know how to show it

Answer 1

You could use the decimal equivalent of 5/4 (or 1.25) and the decimal equivalent of 3/8 (or 0.375) to show this.

Then (1.25)⁴ is equal to 2.4414.

This value times 2 is 4.8828

The value of (0.375)³ is 0.0527

This value times 10 is 0.527

As a result, the first expression sis larger (4.8828 > 0.527).

Answer 2

First I would convert to common denominators

(2 * (5/4)⁴) can also be written as (2 * (40/32)⁴)

( (10 * (3/8)³) can also be written as ( (10 * (12/32)³)

Obviously (40/32)⁴ is much greater than (12/32)³