Solve 17000*(1/0.14-1/0.14*1.14^5)=

$$17000 \times ( \frac{ 1 }{ 0.14 } - \frac{ 1 }{ 0.14 \times { 1.14 }^{ 5 } } )=$$

Evaluate

$$\frac{35116178350000}{601692057}\approx 58362.376470594$$

Solution Steps

Expand \frac{1}{0.14} by multiplying both numerator and the denominator by 100.

$$17000\left(\frac{100}{14}-\frac{1}{0.14\times 1.14^{5}}\right)$$

Reduce the fraction \frac{100}{14} to lowest terms by extracting and canceling out 2.

$$17000\left(\frac{50}{7}-\frac{1}{0.14\times 1.14^{5}}\right)$$

Calculate 1.14 to the power of 5 and get 1.9254145824.

$$17000\left(\frac{50}{7}-\frac{1}{0.14\times 1.9254145824}\right)$$

Multiply 0.14 and 1.9254145824 to get 0.269558041536.

$$17000\left(\frac{50}{7}-\frac{1}{0.269558041536}\right)$$

Expand \frac{1}{0.269558041536} by multiplying both numerator and the denominator by 1000000000000.

$$17000\left(\frac{50}{7}-\frac{1000000000000}{269558041536}\right)$$

Reduce the fraction \frac{1000000000000}{269558041536} to lowest terms by extracting and canceling out 64.

$$17000\left(\frac{50}{7}-\frac{15625000000}{4211844399}\right)$$

Least common multiple of 7 and 4211844399 is 4211844399. Convert \frac{50}{7} and \frac{15625000000}{4211844399} to fractions with denominator 4211844399.

$$17000\left(\frac{30084602850}{4211844399}-\frac{15625000000}{4211844399}\right)$$

Since \frac{30084602850}{4211844399} and \frac{15625000000}{4211844399} have the same denominator, subtract them by subtracting their numerators.

$$17000\times \frac{30084602850-15625000000}{4211844399}$$

Subtract 15625000000 from 30084602850 to get 14459602850.

$$17000\times \frac{14459602850}{4211844399}$$

Reduce the fraction \frac{14459602850}{4211844399} to lowest terms by extracting and canceling out 7.

$$17000\times \frac{2065657550}{601692057}$$

Express 17000\times \frac{2065657550}{601692057} as a single fraction.

$$\frac{17000\times 2065657550}{601692057}$$

Multiply 17000 and 2065657550 to get 35116178350000.

$$\frac{35116178350000}{601692057}$$

Factor

$$\frac{17 \cdot 421 \cdot 811 \cdot 2 ^ {4} \cdot 5 ^ {5} \cdot 11 ^ {2}}{3 ^ {5} \cdot 19 ^ {5}} = 58362\frac{226519366}{601692057} = 58362.37647059383$$