Solve (frac{x^{-2}y^{3}z^{-1}}{x^-1y^2z^3})^2=

$$( \frac { x ^ { - 2 } y ^ { 3 } z ^ { - 1 } } { x ^ { - 1 } y ^ { 2 } z ^ { 3 } } ) ^ { 2 } =$$

Evaluate

$$\frac{\left(\frac{y}{x}\right)^{2}}{z^{8}}$$

Solution Steps

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

$$\left(\frac{x^{-2}\times \frac{1}{z}y}{\frac{1}{x}z^{3}}\right)^{2}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{y}{x^{1}z^{4}}\right)^{2}$$

Calculate x to the power of 1 and get x.

$$\left(\frac{y}{xz^{4}}\right)^{2}$$

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

$$\frac{y^{2}}{\left(xz^{4}\right)^{2}}$$

Expand \left(xz^{4}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{y^{2}}{x^{2}z^{8}}$$

Expand

$$\frac{\left(\frac{y}{x}\right)^{2}}{z^{8}}$$

Solution Steps

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

$$\left(\frac{x^{-2}\times \frac{1}{z}y}{\frac{1}{x}z^{3}}\right)^{2}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{y}{x^{1}z^{4}}\right)^{2}$$

Calculate x to the power of 1 and get x.

$$\left(\frac{y}{xz^{4}}\right)^{2}$$

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

$$\frac{y^{2}}{\left(xz^{4}\right)^{2}}$$

Expand \left(xz^{4}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{y^{2}}{x^{2}z^{8}}$$