Solve {l}{x={(1.00*10^2)/(8.00*10^-2)}{{(4.00*10^-3)}{(4.00)}}}{y=5.00*10^-3}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x = \frac{{(1.00 \cdot 10 ^ {2})} {(8.00 \cdot 10 ^ {-2})}}{{(4.00 \cdot 10 ^ {-3})} {(4.00)}} }\\ { y = 5.00 \cdot 10 ^ {-3} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=\frac{1}{200}=0.005$$

Solution Steps

Consider the first equation. Cancel out 2\times 4 in both numerator and denominator.

$$x=\frac{10^{-2}\times 10^{2}}{2\times 10^{-3}}$$

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

$$x=\frac{10^{-2}\times 10^{5}}{2}$$

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

$$x=\frac{10^{3}}{2}$$

Calculate 10 to the power of 3 and get 1000.

$$x=\frac{1000}{2}$$

Divide 1000 by 2 to get 500.

$$x=500$$

Consider the second equation. Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$y=5\times \frac{1}{1000}$$

Multiply 5 and \frac{1}{1000} to get \frac{1}{200}.

$$y=\frac{1}{200}$$

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

$$z=\frac{1}{200}$$

The system is now solved.

$$x=500 y=\frac{1}{200} z=\frac{1}{200}$$