今日喺Facebook見到有人問咗一條看似簡單, 但係又唔可以就咁用計數機㩒個答案出嚟嘅數。想喺依度同大家分享一吓:
\(\begin{align}
&\dfrac{84^{90}-64^{80}}{20^{70}} \\
&= \dfrac{84^{90}}{20^{70}}-\dfrac{64^{80}}{20^{70}} \\
&= (\dfrac{84^{9}}{20^{7}})^{10}-(\dfrac{64^{8}}{20^{7}})^{10} \\
&= (162668553.5)^{10} – (219902.33)^{10}\\
&= 1.297287 \times 10^{82} – 2.644 \times 10^{53} \\
&= 1.297 \times 10^{82}
\end{align}\)
另一個較快嘅方法係利用\(84^{94}\)比\(64^{80}\)大好多好多,
\(\begin{align}
&\dfrac{84^{90}-64^{80}}{20^{70}} \\
&\approx \dfrac{84^{90}}{20^{70}} \\
&= (\dfrac{84^{9}}{20^{7}})^{10} \\
&= (162668553.5)^{10} \\
&= 1.297 \times 10^{82}
\end{align}\)