Why is 1/2 not useful as a benchmark to compare 5/8 and 9/10?

Solution:

1/2 is not a useful benchmark to compare 5/8 and 9/10 because if we observe closely we found that

and

In the first case 1/2 comes four times and in the second case 1/2 comes 5 times in multiplication so logically the second number 9/10 should be smaller than the first number 5/8.

But 9 is greater than 5 it mean second number should be greater than the first number.

Both the above two conclusions are contradictory to each other.

Hence we can not use 1/2 as a benchmark to compare 5/8 and 9/10.

(1/(25^3×2))^(1/3)25^3 = 25×25^2: (1/(25×25^2×2))^(1/3)  | 2 | 5× | 2 | 51 | 2 | 55 | 0 | 06 | 2 | 5: (1/(25×625×2))^(1/3)25×625 = 15625: (1/(15625×2))^(1/3)15625×2 = 31250: (1/31250)^(1/3)(1/31250)^(1/3) = (1^(1/3))/(31250^(1/3)): (1^(1/3))/(31250^(1/3))31250^(1/3) = (2×5^6)^(1/3) = 5^2 2^(1/3): (1^(1/3))/(5^2 2^(1/3))5^2 = 25: (1^(1/3))/(25 2^(1/3))rationalize the denominator. (1^(1/3))/(25 2^(1/3)) = (1^(1/3))/(25 2^(1/3))×(2^(2/3))/(2^(2/3)) = (1^(1/3)×2^(2/3))/(25×2): (1^(1/3)×2^(2/3))/(25×2)25×2 = 50: answer: (1^(1/3)×2^(2/3))/(50)