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

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

Procijeni

$$\frac{211884719464275}{377801998336}\approx 560,835359256$$

Koraci za rješenje

Svedite razlomak \frac{12}{100} na najprostije elemente rastavlјanjem i kraćenjem 4.

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

Saberite 1 i \frac{3}{25} da biste dobili \frac{28}{25}.

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

Izračunajte \frac{28}{25} stepen od 4 i dobijte \frac{614656}{390625}.

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

Podijelite 275 sa \frac{614656}{390625} tako što ćete pomnožiti 275 recipročnom vrijednošću od \frac{614656}{390625}.

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

Pomnožite 275 i \frac{390625}{614656} da biste dobili \frac{107421875}{614656}.

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

Saberite 275 i \frac{107421875}{614656} da biste dobili \frac{276452275}{614656}.

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

Svedite razlomak \frac{12}{100} na najprostije elemente rastavlјanjem i kraćenjem 4.

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

Saberite 1 i \frac{3}{25} da biste dobili \frac{28}{25}.

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

Izračunajte \frac{28}{25} stepen od 8 i dobijte \frac{377801998336}{152587890625}.

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

Podijelite 275 sa \frac{377801998336}{152587890625} tako što ćete pomnožiti 275 recipročnom vrijednošću od \frac{377801998336}{152587890625}.

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

Pomnožite 275 i \frac{152587890625}{377801998336} da biste dobili \frac{41961669921875}{377801998336}.

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

Saberite \frac{276452275}{614656} i \frac{41961669921875}{377801998336} da biste dobili \frac{211884719464275}{377801998336}.

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

Faktor

$$\frac{3 \cdot 5 ^ {2} \cdot 11 \cdot 13 ^ {2} \cdot 19 \cdot 37 \cdot 709 \cdot 3049}{2 ^ {16} \cdot 7 ^ {8}} = 560\frac{315600396115}{377801998336} = 560,8353592556551$$