Question
Number of prime factors in `(216)^(3/5) xx (2500)^(2/5) xx (300)^(1/5)` is :
Answer: Option B
Was this answer helpful ?
`(216)^(3/5) xx (2500)^(2/5) xx (300)^(1/5)` = `(3^3 xx 2^3)^(3/5) xx (5^4 xx 2^2)^(2/5) xx (5^2 xx 2^2 xx3)^(1/5)`
=`3^((3xx3/5)) xx 2^((3xx3/5)) xx 5^((4xx2/5)) xx 2^ ((2xx2/5)) xx 5^((2xx1/5)) xx 2^((2xx1/5)) xx 3^(1/5)`
=`3^(9/5) xx 2^(9/5) xx5^(8/5) xx 2^(4/5) xx 5^(2/5) xx 2^(2/5) xx 3^(1/5)`
=`3^((9/5 + 1/5)) xx 2^((9/5 + 4/5 + 2/5)) xx 5^((8/5 + 2/5))`
=`3^2 xx 2^3 xx 5^2`.
Hence, the number of prime factors = (2 + 3 + 2 ) = 7.
Was this answer helpful ?
More Questions on This Topic :
Latest Videos
Latest Test Papers
Submit Solution