Solve {left(31/8right)}^12{left(8/25right)}^11-2^3

$${ \left(3 \frac{ 1 }{ 8 } \right) }^{ 12 } { \left( \frac{ 8 }{ 25 } \right) }^{ 11 } { -2 }^{ 3 }$$

Evaluate

$$-25$$

Solution Steps

Multiply 3 and 8 to get 24.

$$\left(\frac{24+1}{8}\right)^{12}\times \left(\frac{8}{25}\right)^{11}\left(-2\right)^{3}$$

Add 24 and 1 to get 25.

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

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

$$\frac{59604644775390625}{68719476736}\times \left(\frac{8}{25}\right)^{11}\left(-2\right)^{3}$$

Calculate \frac{8}{25} to the power of 11 and get \frac{8589934592}{2384185791015625}.

$$\frac{59604644775390625}{68719476736}\times \frac{8589934592}{2384185791015625}\left(-2\right)^{3}$$

Multiply \frac{59604644775390625}{68719476736} and \frac{8589934592}{2384185791015625} to get \frac{25}{8}.

$$\frac{25}{8}\left(-2\right)^{3}$$

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

$$\frac{25}{8}\left(-8\right)$$

Multiply \frac{25}{8} and -8 to get -25.

$$-25$$

Factor

$$-25$$