Which is greater: 2^3,000,000 or 3^2,000,000 ???

Answer

The Answer : 3^(2,000,000)

Here’s a simple way.

3,000,000 = 3 x 1,000,000
2,000,000 = 2 x 1,000,000

So,
2^3,000,000 = (2)^(3 x 1,000,000)
2^3,000,000 = (2^3)^(1,000,000)
2^3,000,000 = 8^(1,000,000)

Similarly,
3^2,000,000 = (3)^(2 x 1,000,000)
3^2,000,000 = (3^2)^(1,000,000)
3^2,000,000 = 9^(1,000,000)

So, which is bigger, 8^(1,000,000) or 9^(1,000,000)?

Its obvious now, with a bit of “manipulation”.

9^(1,000,000) is bigger.