Calculate the total number of prime factors i | vedclass

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Question

(B) To find the total number of prime factors,we first express all bases as prime numbers.Given expression: $(4)^{11} 	imes (5)^{5} 	imes (3)^{2}

Vedclass · Accepted Answer

$31$

Vedclass · Answer

(B) To find the total number of prime factors,we first express all bases as prime numbers.Given expression: $(4)^{11} 	imes (5)^{5} 	imes (3)^{2} 	imes (13)^{2}$.Since $4 = 2^2$,we can rewrite the expression as:$(2^2)^{11} 	imes (5)^{5} 	imes (3)^{2} 	imes (13)^{2} = (2)^{22} 	imes (5)^{5} 	imes (3)^{2} 	imes (13)^{2}$.The total number of prime factors is the sum of the exponents of these prime bases:Total prime factors $= 22 + 5 + 2 + 2 = 31$.

Calculate the total number of prime factors in the expression $(4)^{11} \times (5)^{5} \times (3)^{2} \times (13)^{2}$.

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