Solve 25000/0.408*(1-1/1.88^10)+500,000/108^10

$$\frac { 25000 } { 0.408 } \times ( 1 - \frac { 1 } { 1.88 ^ { 10 } } ) + \frac { 500,000 } { 108 ^ { 10 } }$$

Evaluate

$$\frac{368983366818670854319753158473083156765625}{6032746512873236570395354308038393856}\approx 61163.413054286$$

Solution Steps

Expand \frac{25000}{0.408} by multiplying both numerator and the denominator by 1000.

$$\frac{25000000}{408}\left(1-\frac{1}{1.88^{10}}\right)+\frac{500000}{108^{10}}$$

Reduce the fraction \frac{25000000}{408} to lowest terms by extracting and canceling out 8.

$$\frac{3125000}{51}\left(1-\frac{1}{1.88^{10}}\right)+\frac{500000}{108^{10}}$$

Calculate 1.88 to the power of 10 and get 551.54187683317729460224.

$$\frac{3125000}{51}\left(1-\frac{1}{551.54187683317729460224}\right)+\frac{500000}{108^{10}}$$

Expand \frac{1}{551.54187683317729460224} by multiplying both numerator and the denominator by 100000000000000000000.

$$\frac{3125000}{51}\left(1-\frac{100000000000000000000}{55154187683317729460224}\right)+\frac{500000}{108^{10}}$$

Reduce the fraction \frac{100000000000000000000}{55154187683317729460224} to lowest terms by extracting and canceling out 1048576.

$$\frac{3125000}{51}\left(1-\frac{95367431640625}{52599132235830049}\right)+\frac{500000}{108^{10}}$$

Convert 1 to fraction \frac{52599132235830049}{52599132235830049}.

$$\frac{3125000}{51}\left(\frac{52599132235830049}{52599132235830049}-\frac{95367431640625}{52599132235830049}\right)+\frac{500000}{108^{10}}$$

Since \frac{52599132235830049}{52599132235830049} and \frac{95367431640625}{52599132235830049} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3125000}{51}\times \frac{52599132235830049-95367431640625}{52599132235830049}+\frac{500000}{108^{10}}$$

Subtract 95367431640625 from 52599132235830049 to get 52503764804189424.

$$\frac{3125000}{51}\times \frac{52503764804189424}{52599132235830049}+\frac{500000}{108^{10}}$$

Multiply \frac{3125000}{51} times \frac{52503764804189424}{52599132235830049} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3125000\times 52503764804189424}{51\times 52599132235830049}+\frac{500000}{108^{10}}$$

Do the multiplications in the fraction \frac{3125000\times 52503764804189424}{51\times 52599132235830049}.

$$\frac{164074265013091950000000}{2682555744027332499}+\frac{500000}{108^{10}}$$

Reduce the fraction \frac{164074265013091950000000}{2682555744027332499} to lowest terms by extracting and canceling out 3.

$$\frac{54691421671030650000000}{894185248009110833}+\frac{500000}{108^{10}}$$

Calculate 108 to the power of 10 and get 215892499727278669824.

$$\frac{54691421671030650000000}{894185248009110833}+\frac{500000}{215892499727278669824}$$

Reduce the fraction \frac{500000}{215892499727278669824} to lowest terms by extracting and canceling out 32.

$$\frac{54691421671030650000000}{894185248009110833}+\frac{15625}{6746640616477458432}$$

Least common multiple of 894185248009110833 and 6746640616477458432 is 6032746512873236570395354308038393856. Convert \frac{54691421671030650000000}{894185248009110833} and \frac{15625}{6746640616477458432} to fractions with denominator 6032746512873236570395354308038393856.

$$\frac{368983366818670854305781513972940800000000}{6032746512873236570395354308038393856}+\frac{13971644500142356765625}{6032746512873236570395354308038393856}$$

Since \frac{368983366818670854305781513972940800000000}{6032746512873236570395354308038393856} and \frac{13971644500142356765625}{6032746512873236570395354308038393856} have the same denominator, add them by adding their numerators.

$$\frac{368983366818670854305781513972940800000000+13971644500142356765625}{6032746512873236570395354308038393856}$$

Add 368983366818670854305781513972940800000000 and 13971644500142356765625 to get 368983366818670854319753158473083156765625.

$$\frac{368983366818670854319753158473083156765625}{6032746512873236570395354308038393856}$$

Factor

$$\frac{33391 \cdot 707224565793026105132047621882463 \cdot 5 ^ {6}}{17 \cdot 2 ^ {15} \cdot 3 ^ {30} \cdot 47 ^ {10}} = 61163\frac{2.491851805073572 \times 10^{36}}{6.032746512873236 \times 10^{36}} = 61163.41305428626$$