Question

If y=m^4=n^3 and y is greater than 1, then mn=

Answer 1

The useful property in multiplication is that 1 raised to any number will always be equal to 1. Thus, if y is equal to 1, m and n are also equal to 1. But if y is greater than 1, then m and n would also, consequently, be greater than 1 but less than y. This is because the base number of an exponent must be less in value than the answer. However, if m and n are multiplied, then the product would be greater than 1 but still less than y. 

Let's take an example to prove this point.

Suppose y=5, then
m = ⁴√5 = 1.49
n = ∛5 = 1.7

Then, m×n = 2.5 which is less than y but greater than 1