Solve rho=4/16(0.138*10^-8)^3sqrt{2*6.022*10^3}

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

Solve for ρ

$$\rho =\frac{7812500000000000000000000000000\sqrt{2}}{989140599}\approx 1.116984124 \cdot 10^{22}$$

Steps for Solving Linear Equation

Multiply 6.022 and 16 to get 96.352.

$$\rho =\frac{4}{96.352\times \left(0.138\times 10^{-8}\right)^{3}\sqrt{2}\times 10^{3}}$$

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

$$\rho =\frac{4}{96.352\times \left(0.138\times \frac{1}{100000000}\right)^{3}\sqrt{2}\times 10^{3}}$$

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

$$\rho =\frac{4}{96.352\times \left(\frac{69}{50000000000}\right)^{3}\sqrt{2}\times 10^{3}}$$

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

$$\rho =\frac{4}{96.352\times \frac{328509}{125000000000000000000000000000000}\sqrt{2}\times 10^{3}}$$

Multiply 96.352 and \frac{328509}{125000000000000000000000000000000} to get \frac{989140599}{3906250000000000000000000000000000}.

$$\rho =\frac{4}{\frac{989140599}{3906250000000000000000000000000000}\sqrt{2}\times 10^{3}}$$

Calculate 10 to the power of 3 and get 1000.

$$\rho =\frac{4}{\frac{989140599}{3906250000000000000000000000000000}\sqrt{2}\times 1000}$$

Multiply \frac{989140599}{3906250000000000000000000000000000} and 1000 to get \frac{989140599}{3906250000000000000000000000000}.

$$\rho =\frac{4}{\frac{989140599}{3906250000000000000000000000000}\sqrt{2}}$$

Rationalize the denominator of \frac{4}{\frac{989140599}{3906250000000000000000000000000}\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\rho =\frac{4\sqrt{2}}{\frac{989140599}{3906250000000000000000000000000}\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\rho =\frac{4\sqrt{2}}{\frac{989140599}{3906250000000000000000000000000}\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\rho =\frac{2\sqrt{2}}{\frac{989140599}{3906250000000000000000000000000}}$$

Divide 2\sqrt{2} by \frac{989140599}{3906250000000000000000000000000} to get \frac{7812500000000000000000000000000}{989140599}\sqrt{2}.

$$\rho =\frac{7812500000000000000000000000000}{989140599}\sqrt{2}$$

Assign ρ

$$\rho ≔\frac{7812500000000000000000000000000\sqrt{2}}{989140599}$$