Solve (2)(12/5)^11*(-5/6)^13*(1/2)^12

$$( 2 ) ( \frac { 12 } { 5 } ) ^ { 11 } \times ( - \frac { 5 } { 6 } ) ^ { 13 } \times ( \frac { 1 } { 2 } ) ^ { 12 }$$

Evaluate

$$-\frac{25}{36}\approx -0.694444444$$

Solution Steps

Calculate \frac{12}{5} to the power of 11 and get \frac{743008370688}{48828125}.

$$2\times \frac{743008370688}{48828125}\left(-\frac{5}{6}\right)^{13}\times \left(\frac{1}{2}\right)^{12}$$

Express 2\times \frac{743008370688}{48828125} as a single fraction.

$$\frac{2\times 743008370688}{48828125}\left(-\frac{5}{6}\right)^{13}\times \left(\frac{1}{2}\right)^{12}$$

Multiply 2 and 743008370688 to get 1486016741376.

$$\frac{1486016741376}{48828125}\left(-\frac{5}{6}\right)^{13}\times \left(\frac{1}{2}\right)^{12}$$

Calculate -\frac{5}{6} to the power of 13 and get -\frac{1220703125}{13060694016}.

$$\frac{1486016741376}{48828125}\left(-\frac{1220703125}{13060694016}\right)\times \left(\frac{1}{2}\right)^{12}$$

Multiply \frac{1486016741376}{48828125} times -\frac{1220703125}{13060694016} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1486016741376\left(-1220703125\right)}{48828125\times 13060694016}\times \left(\frac{1}{2}\right)^{12}$$

Do the multiplications in the fraction \frac{1486016741376\left(-1220703125\right)}{48828125\times 13060694016}.

$$\frac{-1813985280000000000000}{637729200000000000}\times \left(\frac{1}{2}\right)^{12}$$

Reduce the fraction \frac{-1813985280000000000000}{637729200000000000} to lowest terms by extracting and canceling out 70858800000000000.

$$-\frac{25600}{9}\times \left(\frac{1}{2}\right)^{12}$$

Calculate \frac{1}{2} to the power of 12 and get \frac{1}{4096}.

$$-\frac{25600}{9}\times \frac{1}{4096}$$

Multiply -\frac{25600}{9} times \frac{1}{4096} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-25600}{9\times 4096}$$

Do the multiplications in the fraction \frac{-25600}{9\times 4096}.

$$\frac{-25600}{36864}$$

Reduce the fraction \frac{-25600}{36864} to lowest terms by extracting and canceling out 1024.

$$-\frac{25}{36}$$

Factor

$$-\frac{25}{36} = -0.6944444444444444$$