Solve (1*10^-3)*(10*10^3)=mu(2.3*10^22)*(4*10^2)

$$( 1 \times 10 ^ { - 3 } ) \times ( 10 \times 10 ^ { 3 } ) = \mu ( 2.3 \times 10 ^ { 22 } ) \times ( 4 \times 10 ^ { 2 } )$$

Solve for μ

$$\mu =\frac{1}{920000000000000000000000}\approx 1.086956522 \cdot 10^{-24}$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add -3 and 1 to get -2.

$$1\times 10^{-2}\times 10^{3}=\mu \times 2.3\times 10^{22}\times 4\times 10^{2}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$1\times 10^{1}=\mu \times 2.3\times 10^{22}\times 4\times 10^{2}$$

To multiply powers of the same base, add their exponents. Add 22 and 2 to get 24.

$$1\times 10^{1}=\mu \times 2.3\times 10^{24}\times 4$$

Calculate 10 to the power of 1 and get 10.

$$1\times 10=\mu \times 2.3\times 10^{24}\times 4$$

Multiply 1 and 10 to get 10.

$$10=\mu \times 2.3\times 10^{24}\times 4$$

Calculate 10 to the power of 24 and get 1000000000000000000000000.

$$10=\mu \times 2.3\times 1000000000000000000000000\times 4$$

Multiply 2.3 and 1000000000000000000000000 to get 2300000000000000000000000.

$$10=\mu \times 2300000000000000000000000\times 4$$

Multiply 2300000000000000000000000 and 4 to get 9200000000000000000000000.

$$10=\mu \times 9200000000000000000000000$$

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

$$\mu \times 9200000000000000000000000=10$$

Divide both sides by 9200000000000000000000000.

$$\mu =\frac{10}{9200000000000000000000000}$$

Reduce the fraction \frac{10}{9200000000000000000000000} to lowest terms by extracting and canceling out 10.

$$\mu =\frac{1}{920000000000000000000000}$$