find the number of prime factors in (1/6)12x(8)25x(3/4)15 Share with your friends Share 0 Vijay Kumar Gupta answered this Consider the following expression. 1612×825×3415First express the above as a product of power of primes. = 12×312×2×2×225×32×215 = 1122×312×2325×3152215 Since abn=anbn = 1212× 312×23×25×31522×15 Since a×bn=an×bn and amn=am×n = 2-12 ×3-12×275×315×2-30 Since an=1 a-n and a-n=1 an = 2-12+75-30 ×3-12+15 = 233 ×33The number of prime factors equals the sum of the exponents of the primes in the prime factorization of a number.So the number of prime factors are, 33+3=36 3 View Full Answer