Solve rho=4*106*4/16left(0.13810^-8right)^3sqrt{26.02210^23}

$$\rho = \frac{ 4 \cdot 106 \cdot 4 }{ 16 { \left(0.138 { 10 }^{ -8 } \right) }^{ 3 } \sqrt{ 2 } 6.022 { 10 }^{ 23 } }$$

Solve for ρ

$$\rho =\frac{33125000000000\sqrt{2}}{989140599}\approx 47360.126862621$$

Steps for Solving Linear Equation

Cancel out 2\times 2\times 4 in both numerator and denominator.

$$\rho =\frac{2\times 53}{6.022\sqrt{2}\times 10^{23}\times \left(0.138\times 10^{-8}\right)^{3}}$$

Multiply 2 and 53 to get 106.

$$\rho =\frac{106}{6.022\sqrt{2}\times 10^{23}\times \left(0.138\times 10^{-8}\right)^{3}}$$

Calculate 10 to the power of 23 and get 100000000000000000000000.

$$\rho =\frac{106}{6.022\sqrt{2}\times 100000000000000000000000\times \left(0.138\times 10^{-8}\right)^{3}}$$

Multiply 6.022 and 100000000000000000000000 to get 602200000000000000000000.

$$\rho =\frac{106}{602200000000000000000000\sqrt{2}\times \left(0.138\times 10^{-8}\right)^{3}}$$

Calculate 10 to the power of -8 and get \frac{1}{100000000}.

$$\rho =\frac{106}{602200000000000000000000\sqrt{2}\times \left(0.138\times \frac{1}{100000000}\right)^{3}}$$

Multiply 0.138 and \frac{1}{100000000} to get \frac{69}{50000000000}.

$$\rho =\frac{106}{602200000000000000000000\sqrt{2}\times \left(\frac{69}{50000000000}\right)^{3}}$$

Calculate \frac{69}{50000000000} to the power of 3 and get \frac{328509}{125000000000000000000000000000000}.

$$\rho =\frac{106}{602200000000000000000000\sqrt{2}\times \frac{328509}{125000000000000000000000000000000}}$$

Multiply 602200000000000000000000 and \frac{328509}{125000000000000000000000000000000} to get \frac{989140599}{625000000000}.

$$\rho =\frac{106}{\frac{989140599}{625000000000}\sqrt{2}}$$

Rationalize the denominator of \frac{106}{\frac{989140599}{625000000000}\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\rho =\frac{106\sqrt{2}}{\frac{989140599}{625000000000}\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\rho =\frac{106\sqrt{2}}{\frac{989140599}{625000000000}\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\rho =\frac{53\sqrt{2}}{\frac{989140599}{625000000000}}$$

Divide 53\sqrt{2} by \frac{989140599}{625000000000} to get \frac{33125000000000}{989140599}\sqrt{2}.

$$\rho =\frac{33125000000000}{989140599}\sqrt{2}$$

Assign ρ

$$\rho ≔\frac{33125000000000\sqrt{2}}{989140599}$$