Solve (z/3)^11*(-3/2)^12

$$( \frac { z } { 3 } ) ^ { 11 } \times ( - \frac { 3 } { 2 } ) ^ { 12 }$$

Evaluate

$$\frac{3z^{11}}{4096}$$

Solution Steps

To raise \frac{z}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{z^{11}}{3^{11}}\left(-\frac{3}{2}\right)^{12}$$

Calculate -\frac{3}{2} to the power of 12 and get \frac{531441}{4096}.

$$\frac{z^{11}}{3^{11}}\times \frac{531441}{4096}$$

Multiply \frac{z^{11}}{3^{11}} times \frac{531441}{4096} by multiplying numerator times numerator and denominator times denominator.

$$\frac{z^{11}\times 531441}{3^{11}\times 4096}$$

Calculate 3 to the power of 11 and get 177147.

$$\frac{z^{11}\times 531441}{177147\times 4096}$$

Multiply 177147 and 4096 to get 725594112.

$$\frac{z^{11}\times 531441}{725594112}$$

Divide z^{11}\times 531441 by 725594112 to get z^{11}\times \frac{3}{4096}.

$$z^{11}\times \frac{3}{4096}$$

Expand

$$\frac{3z^{11}}{4096}$$

Solution Steps

To raise \frac{z}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{z^{11}}{3^{11}}\left(-\frac{3}{2}\right)^{12}$$

Calculate -\frac{3}{2} to the power of 12 and get \frac{531441}{4096}.

$$\frac{z^{11}}{3^{11}}\times \frac{531441}{4096}$$

Multiply \frac{z^{11}}{3^{11}} times \frac{531441}{4096} by multiplying numerator times numerator and denominator times denominator.

$$\frac{z^{11}\times 531441}{3^{11}\times 4096}$$

Calculate 3 to the power of 11 and get 177147.

$$\frac{z^{11}\times 531441}{177147\times 4096}$$

Multiply 177147 and 4096 to get 725594112.

$$\frac{z^{11}\times 531441}{725594112}$$

Divide z^{11}\times 531441 by 725594112 to get z^{11}\times \frac{3}{4096}.

$$z^{11}\times \frac{3}{4096}$$