+980 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?
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.
