Calculate the total number of prime factors i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 $(4)^{11} \times (5)^{5} \times (3)^{2} \times (13)^{2}$.

Similar Questions

On simplification of $\frac{(2.644)^{2}-(2.356)^{2}}{0.288},$ we get

If $\frac{x}{y} = \frac{3}{4},$ the ratio of $(2x + 3y)$ and $(3y - 2x)$ is

The simplification of $\left[\frac{1}{2}+\frac{1}{2}\left\{\frac{3}{4}-\frac{1}{2}\left(\frac{7}{8}-\frac{3}{4}\right)\right\}\right]$ yields

If the numerator of a fraction is increased by $2$ and the denominator is increased by $3,$ the fraction becomes $\frac{7}{9},$ and if both the numerator and the denominator are decreased by $1,$ the fraction becomes $\frac{4}{5}.$ What is the original fraction?

If $\frac{a}{a+b}=\frac{17}{23},$ what is $\frac{a+b}{a-b}$ equal to?

Vedclass Test Series

Exam Paper Generator

Online Exam Module