Resolver 275+275/(1+12%)^4+275/(1+12%)^8

$$275 + \frac { 275 } { ( 1 + 12 \% ) ^ { 4 } } + \frac { 275 } { ( 1 + 12 \% ) ^ { 8 } }$$

Calcular

$$\frac{211884719464275}{377801998336}\approx 560.835359256$$

Pasos da solución

Reduce a fracción \frac{12}{100} a termos máis baixos extraendo e cancelando 4.

$$275+\frac{275}{\left(1+\frac{3}{25}\right)^{4}}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Suma 1 e \frac{3}{25} para obter \frac{28}{25}.

$$275+\frac{275}{\left(\frac{28}{25}\right)^{4}}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Calcula \frac{28}{25} á potencia de 4 e obtén \frac{614656}{390625}.

$$275+\frac{275}{\frac{614656}{390625}}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Divide 275 entre \frac{614656}{390625} mediante a multiplicación de 275 polo recíproco de \frac{614656}{390625}.

$$275+275\times \frac{390625}{614656}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Multiplica 275 e \frac{390625}{614656} para obter \frac{107421875}{614656}.

$$275+\frac{107421875}{614656}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Suma 275 e \frac{107421875}{614656} para obter \frac{276452275}{614656}.

$$\frac{276452275}{614656}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Reduce a fracción \frac{12}{100} a termos máis baixos extraendo e cancelando 4.

$$\frac{276452275}{614656}+\frac{275}{\left(1+\frac{3}{25}\right)^{8}}$$

Suma 1 e \frac{3}{25} para obter \frac{28}{25}.

$$\frac{276452275}{614656}+\frac{275}{\left(\frac{28}{25}\right)^{8}}$$

Calcula \frac{28}{25} á potencia de 8 e obtén \frac{377801998336}{152587890625}.

$$\frac{276452275}{614656}+\frac{275}{\frac{377801998336}{152587890625}}$$

Divide 275 entre \frac{377801998336}{152587890625} mediante a multiplicación de 275 polo recíproco de \frac{377801998336}{152587890625}.

$$\frac{276452275}{614656}+275\times \frac{152587890625}{377801998336}$$

Multiplica 275 e \frac{152587890625}{377801998336} para obter \frac{41961669921875}{377801998336}.

$$\frac{276452275}{614656}+\frac{41961669921875}{377801998336}$$

Suma \frac{276452275}{614656} e \frac{41961669921875}{377801998336} para obter \frac{211884719464275}{377801998336}.

$$\frac{211884719464275}{377801998336}$$

Factorizar

$$\frac{3 \cdot 5 ^ {2} \cdot 11 \cdot 13 ^ {2} \cdot 19 \cdot 37 \cdot 709 \cdot 3049}{2 ^ {16} \cdot 7 ^ {8}} = 560\frac{315600396115}{377801998336} = 560.8353592556551$$