Solve {left(x^2y/zright)}^3(z/x^3)

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

Evaluate

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

Solution Steps

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

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

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

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

Cancel out z in both numerator and denominator.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{y^{3}x^{6}}{z^{2}x^{3}}$$

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

$$\frac{x^{3}y^{3}}{z^{2}}$$

Expand

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

Solution Steps

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

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

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

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

Cancel out z in both numerator and denominator.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{y^{3}x^{6}}{z^{2}x^{3}}$$

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

$$\frac{x^{3}y^{3}}{z^{2}}$$