Question Number 192697 by cortano12 last updated on 25/May/23
$$\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\left(\mathrm{9x}−\frac{\mathrm{1}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{2}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{3}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} …\left(\mathrm{9x}−\frac{\mathrm{2013}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} . \\ $$
Answered by AST last updated on 31/May/23
![x^(6039) [(((900−1)/(100)))(((900−2)/(100)))...(((900−2013)/(100)))]^3 =(x^(6039) /(10^(12078) ))(899)^3 (888)^3 ...(−1113)^3 =0](https://www.tinkutara.com/question/Q192699.png)
$${x}^{\mathrm{6039}} \left[\left(\frac{\mathrm{900}−\mathrm{1}}{\mathrm{100}}\right)\left(\frac{\mathrm{900}−\mathrm{2}}{\mathrm{100}}\right)…\left(\frac{\mathrm{900}−\mathrm{2013}}{\mathrm{100}}\right)\right]^{\mathrm{3}} \\ $$$$=\frac{{x}^{\mathrm{6039}} }{\mathrm{10}^{\mathrm{12078}} }\left(\mathrm{899}\right)^{\mathrm{3}} \left(\mathrm{888}\right)^{\mathrm{3}} …\left(−\mathrm{1113}\right)^{\mathrm{3}} =\mathrm{0} \\ $$
Commented by Mingma last updated on 25/May/23
Nice work, sir!
Commented by cortano12 last updated on 27/May/23
$$\mathrm{answer}\:\mathrm{is}\:\mathrm{0}\: \\ $$