Solve 40div0.0585*(1-1.0585^-16+1000div1.0585^16

$$40 \div 0.0585 \times (1- { 1.0585 }^{ -16 } +1000 \div { 1.0585 }^{ 16 }$$

Evaluate

$$\frac{5250657501678728607518642390152094386506678616881945062480000}{19042308205140588496014495597438040266017477189844653877}\approx 275736.399448743$$

Solution Steps

Expand \frac{40}{0.0585} by multiplying both numerator and the denominator by 10000.

$$\frac{400000}{585}\left(1-1.0585^{-16}+\frac{1000}{1.0585^{16}}\right)$$

Reduce the fraction \frac{400000}{585} to lowest terms by extracting and canceling out 5.

$$\frac{80000}{117}\left(1-1.0585^{-16}+\frac{1000}{1.0585^{16}}\right)$$

Calculate 1.0585 to the power of -16 and get \frac{65536000000000000000000000000000000000000000000000000}{162754770984107593983029876901179831333482711024313281}.

$$\frac{80000}{117}\left(1-\frac{65536000000000000000000000000000000000000000000000000}{162754770984107593983029876901179831333482711024313281}+\frac{1000}{1.0585^{16}}\right)$$

Subtract \frac{65536000000000000000000000000000000000000000000000000}{162754770984107593983029876901179831333482711024313281} from 1 to get \frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}.

$$\frac{80000}{117}\left(\frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}+\frac{1000}{1.0585^{16}}\right)$$

Calculate 1.0585 to the power of 16 and get 2.4834407193619933163914470962704442036969407810106396636962890625.

$$\frac{80000}{117}\left(\frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}+\frac{1000}{2.4834407193619933163914470962704442036969407810106396636962890625}\right)$$

Expand \frac{1000}{2.4834407193619933163914470962704442036969407810106396636962890625} by multiplying both numerator and the denominator by 10000000000000000000000000000000000000000000000000000000000000000.

$$\frac{80000}{117}\left(\frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}+\frac{10000000000000000000000000000000000000000000000000000000000000000000}{24834407193619933163914470962704442036969407810106396636962890625}\right)$$

Reduce the fraction \frac{10000000000000000000000000000000000000000000000000000000000000000000}{24834407193619933163914470962704442036969407810106396636962890625} to lowest terms by extracting and canceling out 152587890625.

$$\frac{80000}{117}\left(\frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}+\frac{65536000000000000000000000000000000000000000000000000000}{162754770984107593983029876901179831333482711024313281}\right)$$

Add \frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281} and \frac{65536000000000000000000000000000000000000000000000000000}{162754770984107593983029876901179831333482711024313281} to get \frac{65633218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}.

$$\frac{80000}{117}\times \frac{65633218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}$$

Multiply \frac{80000}{117} and \frac{65633218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281} to get \frac{5250657501678728607518642390152094386506678616881945062480000}{19042308205140588496014495597438040266017477189844653877}.

$$\frac{5250657501678728607518642390152094386506678616881945062480000}{19042308205140588496014495597438040266017477189844653877}$$