Solve (2x/y)^3*(y/4z)^3

$$( \frac { 2 x } { y } ) ^ { 3 } \times ( \frac { y } { 4 z } ) ^ { 3 }$$

Evaluate

$$\frac{\left(\frac{x}{z}\right)^{3}}{8}$$

Solution Steps

To raise \frac{2x}{y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x\right)^{3}}{y^{3}}\times \left(\frac{y}{4z}\right)^{3}$$

To raise \frac{y}{4z} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x\right)^{3}}{y^{3}}\times \frac{y^{3}}{\left(4z\right)^{3}}$$

Multiply \frac{\left(2x\right)^{3}}{y^{3}} times \frac{y^{3}}{\left(4z\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x\right)^{3}y^{3}}{y^{3}\times \left(4z\right)^{3}}$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{\left(2x\right)^{3}}{\left(4z\right)^{3}}$$

Expand \left(2x\right)^{3}.

$$\frac{2^{3}x^{3}}{\left(4z\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{3}}{\left(4z\right)^{3}}$$

Expand \left(4z\right)^{3}.

$$\frac{8x^{3}}{4^{3}z^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{8x^{3}}{64z^{3}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{x^{3}}{8z^{3}}$$

Expand

$$\frac{\left(\frac{x}{z}\right)^{3}}{8}$$

Solution Steps

To raise \frac{2x}{y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x\right)^{3}}{y^{3}}\times \left(\frac{y}{4z}\right)^{3}$$

To raise \frac{y}{4z} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x\right)^{3}}{y^{3}}\times \frac{y^{3}}{\left(4z\right)^{3}}$$

Multiply \frac{\left(2x\right)^{3}}{y^{3}} times \frac{y^{3}}{\left(4z\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x\right)^{3}y^{3}}{y^{3}\times \left(4z\right)^{3}}$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{\left(2x\right)^{3}}{\left(4z\right)^{3}}$$

Expand \left(2x\right)^{3}.

$$\frac{2^{3}x^{3}}{\left(4z\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{3}}{\left(4z\right)^{3}}$$

Expand \left(4z\right)^{3}.

$$\frac{8x^{3}}{4^{3}z^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{8x^{3}}{64z^{3}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{x^{3}}{8z^{3}}$$