Solve (31/8)^12*(8/7)^11*(-2)^3

$$( 3 \frac { 1 } { 8 } ) ^ { 12 } \times ( \frac { 8 } { 7 } ) ^ { 11 } \times ( - 2 ) ^ { 3 }$$

Evaluate

$$-\frac{59604644775390625}{1977326743}\approx -30144054.333154096$$

Solution Steps

Multiply 3 and 8 to get 24.

$$\left(\frac{24+1}{8}\right)^{12}\times \left(\frac{8}{7}\right)^{11}\left(-2\right)^{3}$$

Add 24 and 1 to get 25.

$$\left(\frac{25}{8}\right)^{12}\times \left(\frac{8}{7}\right)^{11}\left(-2\right)^{3}$$

Calculate \frac{25}{8} to the power of 12 and get \frac{59604644775390625}{68719476736}.

$$\frac{59604644775390625}{68719476736}\times \left(\frac{8}{7}\right)^{11}\left(-2\right)^{3}$$

Calculate \frac{8}{7} to the power of 11 and get \frac{8589934592}{1977326743}.

$$\frac{59604644775390625}{68719476736}\times \frac{8589934592}{1977326743}\left(-2\right)^{3}$$

Multiply \frac{59604644775390625}{68719476736} and \frac{8589934592}{1977326743} to get \frac{59604644775390625}{15818613944}.

$$\frac{59604644775390625}{15818613944}\left(-2\right)^{3}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{59604644775390625}{15818613944}\left(-8\right)$$

Multiply \frac{59604644775390625}{15818613944} and -8 to get -\frac{59604644775390625}{1977326743}.

$$-\frac{59604644775390625}{1977326743}$$

Factor

$$-\frac{59604644775390625}{1977326743} = -30144054\frac{658754502}{1977326743} = -30144054.333154093$$