I need explanation please for throwing one 2

784 = 2^4 times 3^2

There are two things we can do to the factor “2” to make 784 a perfect cube.

One, include two “2”s.
Two, throw away a “2”.

Both are possible. However, there is this extra condition that for the m/n which we must introduce, both m and n must be prime numbers.

If you include 2^2, then the number to introduce, m = 2^2 = 4, is clearly not prime.

So, we cannot include two “2”s.

This leaves us with throwing away one “2”, so this goes into the expression for n.

Without the “m and n are prime numbers” stipulation, you could introduce two “2”s as well.

Remember that you need the powers of each prime factor to be multiples of 3 for the number to be a perfect cube.

So, 2^a times 3^b can only be a perfect cube if a and b are multiples of 3.