Solve y=pi/xsqrt{2*10^-10/1.4*10^-3}

$$y= \frac{ \pi }{ x } \sqrt{ \frac{ 2 \times { 10 }^{ -10 } }{ 1.4 \times { 10 }^{ -3 } } }$$

Solve for x

$$x=\frac{\pi \sqrt{7}}{7000y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$yx=\pi \sqrt{\frac{2\times 10^{-10}}{1.4\times 10^{-3}}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$yx=\pi \sqrt{\frac{2}{1.4\times 10^{7}}}$$

Calculate 10 to the power of 7 and get 10000000.

$$yx=\pi \sqrt{\frac{2}{1.4\times 10000000}}$$

Multiply 1.4 and 10000000 to get 14000000.

$$yx=\pi \sqrt{\frac{2}{14000000}}$$

Reduce the fraction \frac{2}{14000000} to lowest terms by extracting and canceling out 2.

$$yx=\pi \sqrt{\frac{1}{7000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{7000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{7000000}}.

$$yx=\pi \times \frac{\sqrt{1}}{\sqrt{7000000}}$$

Calculate the square root of 1 and get 1.

$$yx=\pi \times \frac{1}{\sqrt{7000000}}$$

Factor 7000000=1000^{2}\times 7. Rewrite the square root of the product \sqrt{1000^{2}\times 7} as the product of square roots \sqrt{1000^{2}}\sqrt{7}. Take the square root of 1000^{2}.

$$yx=\pi \times \frac{1}{1000\sqrt{7}}$$

Rationalize the denominator of \frac{1}{1000\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$yx=\pi \times \frac{\sqrt{7}}{1000\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$yx=\pi \times \frac{\sqrt{7}}{1000\times 7}$$

Multiply 1000 and 7 to get 7000.

$$yx=\pi \times \frac{\sqrt{7}}{7000}$$

Express \pi \times \frac{\sqrt{7}}{7000} as a single fraction.

$$yx=\frac{\pi \sqrt{7}}{7000}$$

Multiply both sides of the equation by 7000.

$$7000yx=\pi \sqrt{7}$$

Divide both sides by 7000y.

$$\frac{7000yx}{7000y}=\frac{\pi \sqrt{7}}{7000y}$$

Dividing by 7000y undoes the multiplication by 7000y.

$$x=\frac{\pi \sqrt{7}}{7000y}$$

Variable x cannot be equal to 0.

$$x=\frac{\pi \sqrt{7}}{7000y}\text{, }x\neq 0$$

Solve for y

$$y=\frac{\pi \sqrt{7}}{7000x}$$

$$x\neq 0$$