Solve (frac{x^{2}y^{-2}z}{x^2y^-2z^2})^3

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

Evaluate

$$\frac{1}{z^{3}}$$

Solution Steps

Cancel out y^{-2}zx^{2} in both numerator and denominator.

$$\left(\frac{1}{z}\right)^{3}$$

To raise \frac{1}{z} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{3}}{z^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{z^{3}}$$

Expand

$$\frac{1}{z^{3}}$$

Solution Steps

Cancel out y^{-2}zx^{2} in both numerator and denominator.

$$\left(\frac{1}{z}\right)^{3}$$

To raise \frac{1}{z} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{3}}{z^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{z^{3}}$$