Question Number 10692 by ABD last updated on 23/Feb/17
$${f}\left({x}+{y}\right)={f}\left({x}\right)×{f}\left({y}\right) \\ $$$${f}\left(\mathrm{16}\right)=\mathrm{8}\:\Rightarrow{f}\left(\mathrm{64}\right) \\ $$
Answered by nume1114 last updated on 23/Feb/17
$${f}\left(\mathrm{64}\right)={f}\left(\left(\mathrm{16}+\mathrm{16}\right)+\left(\mathrm{16}+\mathrm{16}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:={f}\left(\mathrm{16}+\mathrm{16}\right)×{f}\left(\mathrm{16}+\mathrm{16}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:={f}\left(\mathrm{16}\right)×{f}\left(\mathrm{16}\right)×{f}\left(\mathrm{16}\right)×{f}\left(\mathrm{16}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\mathrm{8}×\mathrm{8}×\mathrm{8}×\mathrm{8} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\mathrm{4096} \\ $$