Solve 75000div.11(1-(1div(1.11^6)))

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

Evaluate

$$\frac{197821489127500000}{623471517387}\approx 317290.339030369$$

Solution Steps

Expand \frac{75000}{0.11} by multiplying both numerator and the denominator by 100.

$$\frac{7500000}{11}\left(1-\frac{1}{1.11^{6}}\right)$$

Calculate 1.11 to the power of 6 and get 1.870414552161.

$$\frac{7500000}{11}\left(1-\frac{1}{1.870414552161}\right)$$

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

$$\frac{7500000}{11}\left(1-\frac{1000000000000}{1870414552161}\right)$$

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

$$\frac{7500000}{11}\left(\frac{1870414552161}{1870414552161}-\frac{1000000000000}{1870414552161}\right)$$

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

$$\frac{7500000}{11}\times \frac{1870414552161-1000000000000}{1870414552161}$$

Subtract 1000000000000 from 1870414552161 to get 870414552161.

$$\frac{7500000}{11}\times \frac{870414552161}{1870414552161}$$

Multiply \frac{7500000}{11} times \frac{870414552161}{1870414552161} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7500000\times 870414552161}{11\times 1870414552161}$$

Do the multiplications in the fraction \frac{7500000\times 870414552161}{11\times 1870414552161}.

$$\frac{6528109141207500000}{20574560073771}$$

Reduce the fraction \frac{6528109141207500000}{20574560073771} to lowest terms by extracting and canceling out 33.

$$\frac{197821489127500000}{623471517387}$$

Factor

$$\frac{19 \cdot 211 \cdot 229 \cdot 1759 \cdot 2 ^ {5} \cdot 5 ^ {7} \cdot 7 ^ {2}}{3 ^ {5} \cdot 37 ^ {6}} = 317290\frac{211375778770}{623471517387} = 317290.33903036924$$