44 Is there a quicker way of doing calculating the function?

[ern5231]

There is a function f (2 ^ 6) = f (64) = 6 +4 = 10, What is the value of f (2 ^ 9 * 5 ^ 7) =?

The answer can be calculated by direct calculation as 4. Can you suggest a quick approach?

[cbenk121]

Break it down.

2 x 2 x 2 x 2.... * 5 x 5 x 5...

There's 9 2's, and 7 5's. So do this, by the commutive and associative laws.

(5x2)^7*2*2 = 10^7 * 4 = 10000000 * 4 = f(40000000) = 4.