<PRE><B>Question 254315</B>
The number of digits in 2^15 = 32768 = 5.
The number of digits in 5^8 = 390625 = 6.
multiplied together, we get 11 digits.
There can be a shortcut but it involves formulas.
The number of digits of a^b can be approximated by
(i) N = b*log(a)
applying the original information, we get
(ii) 15log(2) ~ 4.515 take the digit and add 1 to get 5.
(iii) 8log(5) ~ 5.591 take the digit and add 1 to get 6.
5 + 6 = 11.</PRE>