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

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

Evaluate

$$-\frac{59604644775390625}{y^{11}}$$

Solution Steps

Multiply 3 and 8 to get 24.

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

Add 24 and 1 to get 25.

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

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

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

To raise \frac{8}{y} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

$$-\frac{59604644775390625}{8589934592}\times \frac{8^{11}}{y^{11}}$$

Calculate 8 to the power of 11 and get 8589934592.

$$-\frac{59604644775390625}{8589934592}\times \frac{8589934592}{y^{11}}$$

Multiply -\frac{59604644775390625}{8589934592} times \frac{8589934592}{y^{11}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-59604644775390625\times 8589934592}{8589934592y^{11}}$$

Cancel out 8589934592 in both numerator and denominator.

$$\frac{-59604644775390625}{y^{11}}$$

Expand

$$-\frac{59604644775390625}{y^{11}}$$

Solution Steps

Multiply 3 and 8 to get 24.

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

Add 24 and 1 to get 25.

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

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

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

To raise \frac{8}{y} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

$$-\frac{59604644775390625}{8589934592}\times \frac{8^{11}}{y^{11}}$$

Calculate 8 to the power of 11 and get 8589934592.

$$-\frac{59604644775390625}{8589934592}\times \frac{8589934592}{y^{11}}$$

Multiply -\frac{59604644775390625}{8589934592} times \frac{8589934592}{y^{11}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-59604644775390625\times 8589934592}{8589934592y^{11}}$$

Cancel out 8589934592 in both numerator and denominator.

$$\frac{-59604644775390625}{y^{11}}$$