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

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

Evaluate

$$\frac{14028098141207500000}{20574560073771}\approx 681817.647177346$$

Solution Steps

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

$$\frac{7500000}{11}\times 1-\frac{1}{1.11^{6}}$$

Multiply \frac{7500000}{11} and 1 to get \frac{7500000}{11}.

$$\frac{7500000}{11}-\frac{1}{1.11^{6}}$$

Calculate 1.11 to the power of 6 and get 1.870414552161.

$$\frac{7500000}{11}-\frac{1}{1.870414552161}$$

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

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

Least common multiple of 11 and 1870414552161 is 20574560073771. Convert \frac{7500000}{11} and \frac{1000000000000}{1870414552161} to fractions with denominator 20574560073771.

$$\frac{14028109141207500000}{20574560073771}-\frac{11000000000000}{20574560073771}$$

Since \frac{14028109141207500000}{20574560073771} and \frac{11000000000000}{20574560073771} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14028109141207500000-11000000000000}{20574560073771}$$

Subtract 11000000000000 from 14028109141207500000 to get 14028098141207500000.

$$\frac{14028098141207500000}{20574560073771}$$

Factor

$$\frac{67 \cdot 193 \cdot 8855857 \cdot 2 ^ {5} \cdot 5 ^ {7} \cdot 7 ^ {2}}{11 \cdot 3 ^ {6} \cdot 37 ^ {6}} = 681817\frac{13315389178893}{20574560073771} = 681817.6471773458$$