Resolver (5/2)^10*[(5/4)^5]^2

$$( \frac { 5 } { 2 } ) ^ { 10 } \cdot [ ( \frac { 5 } { 4 } ) ^ { 5 } ] ^ { 2 }$$

Calcular

$$\frac{95367431640625}{1073741824}=88817.841970013$$

Pasos da solución

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 5 e 2 para obter 10.

$$\left(\frac{5}{2}\right)^{10}\times \left(\frac{5}{4}\right)^{10}$$

Calcula \frac{5}{2} á potencia de 10 e obtén \frac{9765625}{1024}.

$$\frac{9765625}{1024}\times \left(\frac{5}{4}\right)^{10}$$

Calcula \frac{5}{4} á potencia de 10 e obtén \frac{9765625}{1048576}.

$$\frac{9765625}{1024}\times \frac{9765625}{1048576}$$

Multiplica \frac{9765625}{1024} e \frac{9765625}{1048576} para obter \frac{95367431640625}{1073741824}.

$$\frac{95367431640625}{1073741824}$$

Factorizar

$$\frac{5 ^ {20}}{2 ^ {30}} = 88817\frac{904058417}{1073741824} = 88817.84197001252$$