Question

How many prime factors in 25^10 * 36^10 * 20^10 ?

Answer 1

25^10 * 36^10 * 20^10

= (5*5)^10 * (2*2*3*3)^10 * (2*2*5)^10

= 5^10 * 5^10 * 2^10 * 2^10 * 3^10 * 3^10 * 2^10 * 2^10 * 5^10

∴ no. of prime factors = 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 90

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