Solve {l}{x={(5/3)}^2*{(3/5)}^-3}{y=x^-2}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x = {(\frac{5}{3})} ^ {2} \cdot {(\frac{3}{5})} ^ {-3} }\\ { y = x ^ {-2} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=\frac{59049}{9765625}\approx 0.006046618$$

Solution Steps

Consider the first equation. Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$x=\frac{25}{9}\times \left(\frac{3}{5}\right)^{-3}$$

Calculate \frac{3}{5} to the power of -3 and get \frac{125}{27}.

$$x=\frac{25}{9}\times \frac{125}{27}$$

Multiply \frac{25}{9} and \frac{125}{27} to get \frac{3125}{243}.

$$x=\frac{3125}{243}$$

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

$$y=\left(\frac{3125}{243}\right)^{-2}$$

Calculate \frac{3125}{243} to the power of -2 and get \frac{59049}{9765625}.

$$y=\frac{59049}{9765625}$$

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

$$z=\frac{59049}{9765625}$$

The system is now solved.

$$x=\frac{3125}{243} y=\frac{59049}{9765625} z=\frac{59049}{9765625}$$