Solve (75000*.11)div(1-(1div1.11^6))

$$(75000 \times .11) \div (1-(1 \div { 1.11 }^{ 6 } ))$$

Evaluate

$$\frac{1402810914120750}{79128595651}\approx 17728.242269178$$

Solution Steps

Multiply 75000 and 0.11 to get 8250.

$$\frac{8250}{1-\frac{1}{1.11^{6}}}$$

Calculate 1.11 to the power of 6 and get 1.870414552161.

$$\frac{8250}{1-\frac{1}{1.870414552161}}$$

Expand \frac{1}{1.870414552161} by multiplying both numerator and the denominator by 1000000000000.

$$\frac{8250}{1-\frac{1000000000000}{1870414552161}}$$

Convert 1 to fraction \frac{1870414552161}{1870414552161}.

$$\frac{8250}{\frac{1870414552161}{1870414552161}-\frac{1000000000000}{1870414552161}}$$

Since \frac{1870414552161}{1870414552161} and \frac{1000000000000}{1870414552161} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8250}{\frac{1870414552161-1000000000000}{1870414552161}}$$

Subtract 1000000000000 from 1870414552161 to get 870414552161.

$$\frac{8250}{\frac{870414552161}{1870414552161}}$$

Divide 8250 by \frac{870414552161}{1870414552161} by multiplying 8250 by the reciprocal of \frac{870414552161}{1870414552161}.

$$8250\times \frac{1870414552161}{870414552161}$$

Express 8250\times \frac{1870414552161}{870414552161} as a single fraction.

$$\frac{8250\times 1870414552161}{870414552161}$$

Multiply 8250 and 1870414552161 to get 15430920055328250.

$$\frac{15430920055328250}{870414552161}$$

Reduce the fraction \frac{15430920055328250}{870414552161} to lowest terms by extracting and canceling out 11.

$$\frac{1402810914120750}{79128595651}$$

Factor

$$\frac{2 \cdot 3 ^ {7} \cdot 5 ^ {3} \cdot 37 ^ {6}}{19 \cdot 211 \cdot 229 \cdot 1759 \cdot 7 ^ {2}} = 17728\frac{19170419822}{79128595651} = 17728.242269177965$$