Solve (10.344*0.13)div(1-left(1div1.13right)^5

$$(10.344 \times 0.13) \div (1- { \left(1 \div 1.13 \right) }^{ 5 }$$

Evaluate

$$\frac{23822686868349}{8100338262500}\approx 2.940949636$$

Solution Steps

Multiply 10.344 and 0.13 to get 1.34472.

$$\frac{1.34472}{1-\left(\frac{1}{1.13}\right)^{5}}$$

Expand \frac{1}{1.13} by multiplying both numerator and the denominator by 100.

$$\frac{1.34472}{1-\left(\frac{100}{113}\right)^{5}}$$

Calculate \frac{100}{113} to the power of 5 and get \frac{10000000000}{18424351793}.

$$\frac{1.34472}{1-\frac{10000000000}{18424351793}}$$

Subtract \frac{10000000000}{18424351793} from 1 to get \frac{8424351793}{18424351793}.

$$\frac{1.34472}{\frac{8424351793}{18424351793}}$$

Divide 1.34472 by \frac{8424351793}{18424351793} by multiplying 1.34472 by the reciprocal of \frac{8424351793}{18424351793}.

$$1.34472\times \frac{18424351793}{8424351793}$$

Multiply 1.34472 and \frac{18424351793}{8424351793} to get \frac{23822686868349}{8100338262500}.

$$\frac{23822686868349}{8100338262500}$$

Factor

$$\frac{3 \cdot 431 \cdot 113 ^ {5}}{11 \cdot 1721 \cdot 34231 \cdot 2 ^ {2} \cdot 5 ^ {5}} = 2\frac{7622010343349}{8100338262500} = 2.9409496364657524$$