IF `(a^b)^c`=729`, then find the minimum possible value of `a+b+c` (where a,b and c are positive integers).

Options

A. 29
B. 13
C. 12
D. 10

Answer

D

Explanation

`a^(b^(c))=729`
This can be writeen in the following ways :
(i) `27^(2^(1))`
(ii) `9^(3^(1))`
(iii) `729^(1^(1))`
(iv) `3^(6^(1))`
Clearly , `a+b+c` will be minimum in case (iv).
`therefore` Minimum possible value of `a+b+c=3+6+1=10` .
Hence the correct option is (d).