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# What is the value of if x=2?

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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