the number of prime factors in 1 6 12 xx, Latest Questions, General Mathematics

Question:The number of prime factors in` (1/6)^(12) xx (8)^(25) xx (3/4)^(15)` is :

A 33 
B 37 
C 52 
D None

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+ AnswerD

+ Explanation`(1/6)^(12) xx (8)^(25) xx (3/4)^(15)`

`= 1/(2^(12) xx 3^(12)) xx (2^3)^(25) xx 3^(15)/(2^15 xx 2^15)`

`= (2^75 xx 3^15)/(2^42 xx 3^12)`

`= 2^33 xx 3^3`

:. Total number of prime factors 

`= (33 + 3) = 36`

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