Solve rho=2*137.3/(5.08)^3*10^-44*6.023*10^23gcm^-4

$$\rho = \frac { 2 \times 137.3 } { ( 5.08 ) ^ { 3 } \times 10 ^ { - 44 } \times 6.023 \times 10 ^ { 23 } } g cm ^ { - 4 }$$

Solve for c

$$\left\{\begin{matrix}c=\frac{12337410809\rho m^{4}}{4290625000000000000000000000000g}\text{, }&g\neq 0\text{ and }m\neq 0\\c\in \mathrm{R}\text{, }&\rho =0\text{ and }g=0\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add -44 and 23 to get -21.

$$\rho =\frac{2\times 137.3}{5.08^{3}\times 10^{-21}\times 6.023}gcm^{-4}$$

Multiply 2 and 137.3 to get 274.6.

$$\rho =\frac{274.6}{5.08^{3}\times 10^{-21}\times 6.023}gcm^{-4}$$

Calculate 5.08 to the power of 3 and get 131.096512.

$$\rho =\frac{274.6}{131.096512\times 10^{-21}\times 6.023}gcm^{-4}$$

Calculate 10 to the power of -21 and get \frac{1}{1000000000000000000000}.

$$\rho =\frac{274.6}{131.096512\times \frac{1}{1000000000000000000000}\times 6.023}gcm^{-4}$$

Multiply 131.096512 and \frac{1}{1000000000000000000000} to get \frac{2048383}{15625000000000000000000000}.

$$\rho =\frac{274.6}{\frac{2048383}{15625000000000000000000000}\times 6.023}gcm^{-4}$$

Multiply \frac{2048383}{15625000000000000000000000} and 6.023 to get \frac{12337410809}{15625000000000000000000000000}.

$$\rho =\frac{274.6}{\frac{12337410809}{15625000000000000000000000000}}gcm^{-4}$$

Divide 274.6 by \frac{12337410809}{15625000000000000000000000000} by multiplying 274.6 by the reciprocal of \frac{12337410809}{15625000000000000000000000000}.

$$\rho =274.6\times \frac{15625000000000000000000000000}{12337410809}gcm^{-4}$$

Multiply 274.6 and \frac{15625000000000000000000000000}{12337410809} to get \frac{4290625000000000000000000000000}{12337410809}.

$$\rho =\frac{4290625000000000000000000000000}{12337410809}gcm^{-4}$$

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

$$\frac{4290625000000000000000000000000}{12337410809}gcm^{-4}=\rho$$

The equation is in standard form.

$$\frac{4290625000000000000000000000000g}{12337410809m^{4}}c=\rho$$

Divide both sides by \frac{4290625000000000000000000000000}{12337410809}gm^{-4}.

$$\frac{\frac{4290625000000000000000000000000g}{12337410809m^{4}}c\times 12337410809m^{4}}{4290625000000000000000000000000g}=\frac{\rho \times 12337410809m^{4}}{4290625000000000000000000000000g}$$

Dividing by \frac{4290625000000000000000000000000}{12337410809}gm^{-4} undoes the multiplication by \frac{4290625000000000000000000000000}{12337410809}gm^{-4}.

$$c=\frac{\rho \times 12337410809m^{4}}{4290625000000000000000000000000g}$$

Divide \rho by \frac{4290625000000000000000000000000}{12337410809}gm^{-4}.

$$c=\frac{12337410809\rho m^{4}}{4290625000000000000000000000000g}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{12337410809\rho m^{4}}{4290625000000000000000000000000c}\text{, }&c\neq 0\text{ and }m\neq 0\\g\in \mathrm{R}\text{, }&\rho =0\text{ and }c=0\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add -44 and 23 to get -21.

$$\rho =\frac{2\times 137.3}{5.08^{3}\times 10^{-21}\times 6.023}gcm^{-4}$$

Multiply 2 and 137.3 to get 274.6.

$$\rho =\frac{274.6}{5.08^{3}\times 10^{-21}\times 6.023}gcm^{-4}$$

Calculate 5.08 to the power of 3 and get 131.096512.

$$\rho =\frac{274.6}{131.096512\times 10^{-21}\times 6.023}gcm^{-4}$$

Calculate 10 to the power of -21 and get \frac{1}{1000000000000000000000}.

$$\rho =\frac{274.6}{131.096512\times \frac{1}{1000000000000000000000}\times 6.023}gcm^{-4}$$

Multiply 131.096512 and \frac{1}{1000000000000000000000} to get \frac{2048383}{15625000000000000000000000}.

$$\rho =\frac{274.6}{\frac{2048383}{15625000000000000000000000}\times 6.023}gcm^{-4}$$

Multiply \frac{2048383}{15625000000000000000000000} and 6.023 to get \frac{12337410809}{15625000000000000000000000000}.

$$\rho =\frac{274.6}{\frac{12337410809}{15625000000000000000000000000}}gcm^{-4}$$

Divide 274.6 by \frac{12337410809}{15625000000000000000000000000} by multiplying 274.6 by the reciprocal of \frac{12337410809}{15625000000000000000000000000}.

$$\rho =274.6\times \frac{15625000000000000000000000000}{12337410809}gcm^{-4}$$

Multiply 274.6 and \frac{15625000000000000000000000000}{12337410809} to get \frac{4290625000000000000000000000000}{12337410809}.

$$\rho =\frac{4290625000000000000000000000000}{12337410809}gcm^{-4}$$

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

$$\frac{4290625000000000000000000000000}{12337410809}gcm^{-4}=\rho$$

The equation is in standard form.

$$\frac{4290625000000000000000000000000c}{12337410809m^{4}}g=\rho$$

Divide both sides by \frac{4290625000000000000000000000000}{12337410809}cm^{-4}.

$$\frac{\frac{4290625000000000000000000000000c}{12337410809m^{4}}g\times 12337410809m^{4}}{4290625000000000000000000000000c}=\frac{\rho \times 12337410809m^{4}}{4290625000000000000000000000000c}$$

Dividing by \frac{4290625000000000000000000000000}{12337410809}cm^{-4} undoes the multiplication by \frac{4290625000000000000000000000000}{12337410809}cm^{-4}.

$$g=\frac{\rho \times 12337410809m^{4}}{4290625000000000000000000000000c}$$

Divide \rho by \frac{4290625000000000000000000000000}{12337410809}cm^{-4}.

$$g=\frac{12337410809\rho m^{4}}{4290625000000000000000000000000c}$$