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What is the value of $\frac{x^1\cdot x^2\cdot x^3\cdots x^{10}}{x^2\cdot x^4 \cdot x^6 \cdots x^{20}}$ if x = 2?

 Nov 4, 2021
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\(\phantom{=}\quad\dfrac{x^1\cdot x^2\cdot x^3\cdots x^{10}}{x^2\cdot x^4 \cdot x^6 \cdots x^{20}}\\~\\ {=}\quad\dfrac{x^{1+2+3+\dots+10}}{x^{2+4+6+\dots+20}}\\~\\ {=}\quad\dfrac{x^{55}}{x^{110}}\\~\\ {=}\quad x^{55-110}\\~\\ {=}\quad x^{-55}\\~\\ {=}\quad \dfrac{1}{x^{55}} \)

 

 

If  x = 2  we get:

 

\(\dfrac{1}{2^{55}}\ =\ \dfrac{1}{36028797018963968}\)

 

see:  https://www.wolframalpha.com/input/?i=2%5E55

 Nov 4, 2021

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