Solve {l}{x={(1/3)}^{5}*{(1/3)}^-3*{(1/3)}^8/{(1/3)}^9}{y=x^3}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x = {(\frac{1}{3})} ^ {5} \cdot {(\frac{1}{3})} ^ {-3} \cdot {(\frac{1}{3})} ^ {8} / {(\frac{1}{3})} ^ {9} }\\ { y = x ^ {3} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=\frac{1}{27}\approx 0.037037037$$

Solution Steps

Consider the first equation. To multiply powers of the same base, add their exponents. Add 5 and -3 to get 2.

$$x=\frac{\left(\frac{1}{3}\right)^{2}\times \left(\frac{1}{3}\right)^{8}}{\left(\frac{1}{3}\right)^{9}}$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$x=\frac{\left(\frac{1}{3}\right)^{10}}{\left(\frac{1}{3}\right)^{9}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 9 from 10 to get 1.

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

Calculate \frac{1}{3} to the power of 1 and get \frac{1}{3}.

$$x=\frac{1}{3}$$

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

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

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$y=\frac{1}{27}$$

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

$$z=\frac{1}{27}$$

The system is now solved.

$$x=\frac{1}{3} y=\frac{1}{27} z=\frac{1}{27}$$