What is the value of \(m\) in the equation below?

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C

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What is the value of \(m\) in the equation below?

\(\left(\dfrac15\right)^m\cdot \left(\dfrac14\right)^{24}=\dfrac1{2(10)^{47}}\)

A) 23

B) 24

C) 46

D) 47

E) 48

Answer: D

Source: Veritas Prep