Solve {l}{10*10^-6=x*1}{y=6*10^-19}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 10 \cdot 10 ^ {-6} = x \cdot 1 }\\ { y = 6 \cdot 10 ^ {-19} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=\frac{3}{5000000000000000000}=6 \cdot 10^{-19}$$

Solution Steps

Consider the first equation. To multiply powers of the same base, add their exponents. Add 1 and -6 to get -5.

$$10^{-5}=x\times 1$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\frac{1}{100000}=x\times 1$$

Swap sides so that all variable terms are on the left hand side.

$$x\times 1=\frac{1}{100000}$$

Divide both sides by 1.

$$x=\frac{\frac{1}{100000}}{1}$$

Express \frac{\frac{1}{100000}}{1} as a single fraction.

$$x=\frac{1}{100000\times 1}$$

Cancel out 1 in both numerator and denominator.

$$x=\frac{1}{100000}$$

Consider the second equation. Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$y=6\times \frac{1}{10000000000000000000}$$

Multiply 6 and \frac{1}{10000000000000000000} to get \frac{3}{5000000000000000000}.

$$y=\frac{3}{5000000000000000000}$$

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

$$z=\frac{3}{5000000000000000000}$$

The system is now solved.

$$x=\frac{1}{100000} y=\frac{3}{5000000000000000000} z=\frac{3}{5000000000000000000}$$