Resolver (1+15%)^12-1/15%

$$\frac { ( 1 + 15 \% ) ^ { 12 } - 1 } { 15 \% }$$

Avaliar

$$\frac{5939541477340107}{204800000000000}\approx 29,00166737$$

Passos Para a Resolução

Reduza a fração \frac{15}{100} para os termos mais baixos ao retirar e anular 5.

$$\frac{\left(1+\frac{3}{20}\right)^{12}-1}{\frac{15}{100}}$$

Some 1 e \frac{3}{20} para obter \frac{23}{20}.

$$\frac{\left(\frac{23}{20}\right)^{12}-1}{\frac{15}{100}}$$

Calcule \frac{23}{20} elevado a 12 e obtenha \frac{21914624432020321}{4096000000000000}.

$$\frac{\frac{21914624432020321}{4096000000000000}-1}{\frac{15}{100}}$$

Subtraia 1 de \frac{21914624432020321}{4096000000000000} para obter \frac{17818624432020321}{4096000000000000}.

$$\frac{\frac{17818624432020321}{4096000000000000}}{\frac{15}{100}}$$

Reduza a fração \frac{15}{100} para os termos mais baixos ao retirar e anular 5.

$$\frac{\frac{17818624432020321}{4096000000000000}}{\frac{3}{20}}$$

Divida \frac{17818624432020321}{4096000000000000} por \frac{3}{20} ao multiplicar \frac{17818624432020321}{4096000000000000} pelo recíproco de \frac{3}{20}.

$$\frac{17818624432020321}{4096000000000000}\times \frac{20}{3}$$

Multiplique \frac{17818624432020321}{4096000000000000} e \frac{20}{3} para obter \frac{5939541477340107}{204800000000000}.

$$\frac{5939541477340107}{204800000000000}$$

Fatorizar

$$\frac{3 \cdot 7 \cdot 13 \cdot 43 \cdot 67 \cdot 97 \cdot 181 \cdot 463 \cdot 929}{2 ^ {22} \cdot 5 ^ {11}} = 29\frac{341477340107}{204800000000000} = 29,00166736982474$$