Solve {l}{x={(3/2)}^2*{(2/2)}^-4}{y=x^-2}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x = {(\frac{3}{2})} ^ {2} \cdot {(\frac{2}{2})} ^ {-4} }\\ { y = x ^ {-2} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=\frac{16}{81}\approx 0.197530864$$

Solution Steps

Consider the first equation. Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$x=\frac{9}{4}\times \left(\frac{2}{2}\right)^{-4}$$

Divide 2 by 2 to get 1.

$$x=\frac{9}{4}\times 1^{-4}$$

Calculate 1 to the power of -4 and get 1.

$$x=\frac{9}{4}\times 1$$

Multiply \frac{9}{4} and 1 to get \frac{9}{4}.

$$x=\frac{9}{4}$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=\left(\frac{9}{4}\right)^{-2}$$

Calculate \frac{9}{4} to the power of -2 and get \frac{16}{81}.

$$y=\frac{16}{81}$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=\frac{16}{81}$$

The system is now solved.

$$x=\frac{9}{4} y=\frac{16}{81} z=\frac{16}{81}$$