Solve (71/3)^18(3/5)^5*(7/5)

$$( \frac { 71 } { 3 } ) ^ { 18 } ( \frac { 3 } { 5 } ) ^ { 5 } \cdot ( \frac { 7 } { 5 } )$$

Evaluate

$$\frac{14714595126907349182432071013872727}{24911296875}\approx 5.906796102 \cdot 10^{23}$$

Solution Steps

Calculate \frac{71}{3} to the power of 18 and get \frac{2102085018129621311776010144838961}{387420489}.

$$\frac{2102085018129621311776010144838961}{387420489}\times \left(\frac{3}{5}\right)^{5}\times \frac{7}{5}$$

Calculate \frac{3}{5} to the power of 5 and get \frac{243}{3125}.

$$\frac{2102085018129621311776010144838961}{387420489}\times \frac{243}{3125}\times \frac{7}{5}$$

Multiply \frac{2102085018129621311776010144838961}{387420489} times \frac{243}{3125} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2102085018129621311776010144838961\times 243}{387420489\times 3125}\times \frac{7}{5}$$

Do the multiplications in the fraction \frac{2102085018129621311776010144838961\times 243}{387420489\times 3125}.

$$\frac{510806659405497978761570465195867523}{1210689028125}\times \frac{7}{5}$$

Reduce the fraction \frac{510806659405497978761570465195867523}{1210689028125} to lowest terms by extracting and canceling out 243.

$$\frac{2102085018129621311776010144838961}{4982259375}\times \frac{7}{5}$$

Multiply \frac{2102085018129621311776010144838961}{4982259375} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2102085018129621311776010144838961\times 7}{4982259375\times 5}$$

Do the multiplications in the fraction \frac{2102085018129621311776010144838961\times 7}{4982259375\times 5}.

$$\frac{14714595126907349182432071013872727}{24911296875}$$

Factor

$$\frac{7 \cdot 71 ^ {18}}{3 ^ {13} \cdot 5 ^ {6}} = 5.906796101681217 \times 10^{23}\frac{7414581502}{24911296875} = 5.906796101681217 \times 10^{23}$$