Question
Number of prime factors in `(6^12 xx (35)^28 xx (15)^16)/((14)^12 xx (21)^11)` is :
Answer: Option B
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`(6^12 xx (35)^28 xx (15)^16)/((14)^12 xx (21)^11)`
=`((2 xx 3)^12 xx (5 xx 7)^28 xx (3 xx 5)^16)/((2 xx 7)^12 xx (3 xx 7)^11)`
=`(2^12 xx 3^12 xx 5^28 xx 7^28 xx 3^16 xx 5^16)/(2^12 xx 7^12 xx 3^11 xx 7^11)`
=`2^(12 - 12) xx 3^(12 + 16 - 11) xx 5^(28 + 16) xx 7^(28 - 12 - 11)`
=`2^0 xx 3^17 xx 5^44 xx 7^ -5` = `(3^17 xx 5^44)/(7^5)`
Number of prime factors = 17 + 44 + 5 = 66.
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