Resolver 10000*left(10000*0.06div365right)^100

$$10000 \times { \left(10000 \times 0.06 \div 365 \right) }^{ 100 }$$

Calcular

$$\frac{82817974522014550258408423595736849801612281185389443546420186410325491933012122303777028329685801938557337600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2149245430428980534561569914848098377085067912219794750119595237610184023252357660516606846393423039064275276107806457451768466538198307146789480826629151772657629293277672358059930436001}\approx 3.853351197 \cdot 10^{25}$$

Pasos da solución

Multiplica 10000 e 0.06 para obter 600.

$$10000\times \left(\frac{600}{365}\right)^{100}$$

Reduce a fracción \frac{600}{365} a termos máis baixos extraendo e cancelando 5.

$$10000\times \left(\frac{120}{73}\right)^{100}$$

Calcula \frac{120}{73} á potencia de 100 e obtén \frac{8281797452201455025840842359573684980161228118538944354642018641032549193301212230377702832968580193855733760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2149245430428980534561569914848098377085067912219794750119595237610184023252357660516606846393423039064275276107806457451768466538198307146789480826629151772657629293277672358059930436001}.

$$10000\times \frac{8281797452201455025840842359573684980161228118538944354642018641032549193301212230377702832968580193855733760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2149245430428980534561569914848098377085067912219794750119595237610184023252357660516606846393423039064275276107806457451768466538198307146789480826629151772657629293277672358059930436001}$$

Multiplica 10000 e \frac{8281797452201455025840842359573684980161228118538944354642018641032549193301212230377702832968580193855733760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2149245430428980534561569914848098377085067912219794750119595237610184023252357660516606846393423039064275276107806457451768466538198307146789480826629151772657629293277672358059930436001} para obter \frac{82817974522014550258408423595736849801612281185389443546420186410325491933012122303777028329685801938557337600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2149245430428980534561569914848098377085067912219794750119595237610184023252357660516606846393423039064275276107806457451768466538198307146789480826629151772657629293277672358059930436001}.

$$\frac{82817974522014550258408423595736849801612281185389443546420186410325491933012122303777028329685801938557337600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2149245430428980534561569914848098377085067912219794750119595237610184023252357660516606846393423039064275276107806457451768466538198307146789480826629151772657629293277672358059930436001}$$

Factorizar

$$\frac{2 ^ {304} \cdot 3 ^ {100} \cdot 5 ^ {104}}{73 ^ {100}} = 3.8533511970982492 \times 10^{25}\frac{3.4147882721224367 \times 10^{185}}{2.1492454304289805 \times 10^{186}} = 3.8533511970982492 \times 10^{25}$$