Solve 0.3/0.15*1.15^8*left(1.15^8-1/0.15-8right)

$$\frac{ 0.3 }{ 0.15 \times { 1.15 }^{ 8 } } \times \left( \frac{ { 1.15 }^{ 8 } -1 }{ 0.15 } -8 \right)$$

Evaluate

$$\frac{293213137080}{78310985281}\approx 3.744214634$$

Solution Steps

Calculate 1.15 to the power of 8 and get 3.0590228625390625.

$$\frac{0.3}{0.15\times 3.0590228625390625}\left(\frac{1.15^{8}-1}{0.15}-8\right)$$

Multiply 0.15 and 3.0590228625390625 to get 0.458853429380859375.

$$\frac{0.3}{0.458853429380859375}\left(\frac{1.15^{8}-1}{0.15}-8\right)$$

Expand \frac{0.3}{0.458853429380859375} by multiplying both numerator and the denominator by 1000000000000000000.

$$\frac{300000000000000000}{458853429380859375}\left(\frac{1.15^{8}-1}{0.15}-8\right)$$

Reduce the fraction \frac{300000000000000000}{458853429380859375} to lowest terms by extracting and canceling out 5859375.

$$\frac{51200000000}{78310985281}\left(\frac{1.15^{8}-1}{0.15}-8\right)$$

Calculate 1.15 to the power of 8 and get 3.0590228625390625.

$$\frac{51200000000}{78310985281}\left(\frac{3.0590228625390625-1}{0.15}-8\right)$$

Subtract 1 from 3.0590228625390625 to get 2.0590228625390625.

$$\frac{51200000000}{78310985281}\left(\frac{2.0590228625390625}{0.15}-8\right)$$

Expand \frac{2.0590228625390625}{0.15} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{51200000000}{78310985281}\left(\frac{20590228625390625}{1500000000000000}-8\right)$$

Reduce the fraction \frac{20590228625390625}{1500000000000000} to lowest terms by extracting and canceling out 1171875.

$$\frac{51200000000}{78310985281}\left(\frac{17570328427}{1280000000}-8\right)$$

Convert 8 to fraction \frac{10240000000}{1280000000}.

$$\frac{51200000000}{78310985281}\left(\frac{17570328427}{1280000000}-\frac{10240000000}{1280000000}\right)$$

Since \frac{17570328427}{1280000000} and \frac{10240000000}{1280000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{51200000000}{78310985281}\times \frac{17570328427-10240000000}{1280000000}$$

Subtract 10240000000 from 17570328427 to get 7330328427.

$$\frac{51200000000}{78310985281}\times \frac{7330328427}{1280000000}$$

Multiply \frac{51200000000}{78310985281} times \frac{7330328427}{1280000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{51200000000\times 7330328427}{78310985281\times 1280000000}$$

Do the multiplications in the fraction \frac{51200000000\times 7330328427}{78310985281\times 1280000000}.

$$\frac{375312815462400000000}{100238061159680000000}$$

Reduce the fraction \frac{375312815462400000000}{100238061159680000000} to lowest terms by extracting and canceling out 1280000000.

$$\frac{293213137080}{78310985281}$$

Factor

$$\frac{3 \cdot 5 \cdot 2443442809 \cdot 2 ^ {3}}{23 ^ {8}} = 3\frac{58280181237}{78310985281} = 3.7442146338457585$$