Solve {l}{F=6}{a=7*10^-11*3*10^6*2*10^6}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { F = 6 }\\ { a = 7 \cdot 10 ^ {-11} \cdot 3 \cdot 10 ^ {6} \cdot 2 \cdot 10 ^ {6} }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for F, a, b

$$b=420$$

Solution Steps

Consider the second equation. To multiply powers of the same base, add their exponents. Add -11 and 6 to get -5.

$$a=7\times 10^{-5}\times 3\times 2\times 10^{6}$$

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

$$a=7\times 10^{1}\times 3\times 2$$

Calculate 10 to the power of 1 and get 10.

$$a=7\times 10\times 3\times 2$$

Multiply 7 and 10 to get 70.

$$a=70\times 3\times 2$$

Multiply 70 and 3 to get 210.

$$a=210\times 2$$

Multiply 210 and 2 to get 420.

$$a=420$$

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

$$b=420$$

The system is now solved.

$$F=6 a=420 b=420$$