Question 2

Calculate the total numbers of prime factors in the expression $$(9)^{11} \times (5)^7 \times (7)^5 \times (3)^2 \times (17)^2$$

Solution

Expression : $$(9)^{11} \times (5)^7 \times (7)^5 \times (3)^2 \times (17)^2$$

Prime factorization = $$(3)^{22} \times (5)^{7}\times(7)^5 \times (3)^{2} \times (17)^{2}$$

= $$(3)^{24} \times (5)^{7}\times(7)^5 \times (17)^{2}$$

Now, there are 4 distinct factors = $$3,5,7,17$$

Total number of prime factors = $$24+7+5+2=38$$

=> Ans - (D)

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