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What is the value of\(\frac{x^1\cdot x^2\cdot x^3\cdots x^{15}}{x^2\cdot x^4 \cdot x^6 \cdots x^{20}}\)if x=2?

 Apr 15, 2020
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Notice all even powers of x will cancel with those in the numerator except \(x^{16},x^{18},x^{20}\)

All odd power in the numerator will stay the same tho. 

Notice \(x^{16}\) will cancel \(x^9,x^7\) 

 \(x^{20}\) will cancel \(x^{15},x^5\) 

\(x^{18}\) will cancel \(x^{13},x,x^{3}\) also will remove 1 power of \(x^{11}\) this becomes \(x^{10}\)

Now if x=2,  \(2^{10}=1024\)

The usual way to solve it is to find terms that cancel.

 Apr 15, 2020
edited by Guest  Apr 15, 2020

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