Solve (2/5)^10*(-5/6)^10*(1/2)^11

$$( \frac { 2 } { 5 } ) ^ { 10 } \times ( - \frac { 5 } { 6 } ) ^ { 10 } \times ( \frac { 1 } { 2 } ) ^ { 11 }$$

Evaluate

$$\frac{1}{120932352}\approx 8.269085844 \cdot 10^{-9}$$

Solution Steps

Calculate \frac{2}{5} to the power of 10 and get \frac{1024}{9765625}.

$$\frac{1024}{9765625}\left(-\frac{5}{6}\right)^{10}\times \left(\frac{1}{2}\right)^{11}$$

Calculate -\frac{5}{6} to the power of 10 and get \frac{9765625}{60466176}.

$$\frac{1024}{9765625}\times \frac{9765625}{60466176}\times \left(\frac{1}{2}\right)^{11}$$

Multiply \frac{1024}{9765625} times \frac{9765625}{60466176} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1024\times 9765625}{9765625\times 60466176}\times \left(\frac{1}{2}\right)^{11}$$

Cancel out 9765625 in both numerator and denominator.

$$\frac{1024}{60466176}\times \left(\frac{1}{2}\right)^{11}$$

Reduce the fraction \frac{1024}{60466176} to lowest terms by extracting and canceling out 1024.

$$\frac{1}{59049}\times \left(\frac{1}{2}\right)^{11}$$

Calculate \frac{1}{2} to the power of 11 and get \frac{1}{2048}.

$$\frac{1}{59049}\times \frac{1}{2048}$$

Multiply \frac{1}{59049} times \frac{1}{2048} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{59049\times 2048}$$

Do the multiplications in the fraction \frac{1\times 1}{59049\times 2048}.

$$\frac{1}{120932352}$$

Factor

$$\frac{1}{2 ^ {11} \cdot 3 ^ {10}} = 8.2690858439601 \times 10^{-9}$$