Solve frac{P_{2}}{P_{1}}=(frac{V_{2}}{V_{1}})^2

$$\frac { P _ { 2 } } { P _ { 1 } } = ( \frac { V _ { 2 } } { V _ { 1 } } ) ^ { 2 }$$

Solve for P_1

$$\left\{\begin{matrix}P_{1}=\left(\frac{V_{1}}{V_{2}}\right)^{2}P_{2}\text{, }&V_{1}\neq 0\text{ and }P_{2}\neq 0\text{ and }V_{2}\neq 0\\P_{1}\neq 0\text{, }&V_{2}=0\text{ and }P_{2}=0\text{ and }V_{1}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable P_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by P_{1}.

$$P_{2}=P_{1}\times \left(\frac{V_{2}}{V_{1}}\right)^{2}$$

To raise \frac{V_{2}}{V_{1}} to a power, raise both numerator and denominator to the power and then divide.

$$P_{2}=P_{1}\times \frac{V_{2}^{2}}{V_{1}^{2}}$$

Express P_{1}\times \frac{V_{2}^{2}}{V_{1}^{2}} as a single fraction.

$$P_{2}=\frac{P_{1}V_{2}^{2}}{V_{1}^{2}}$$

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

$$\frac{P_{1}V_{2}^{2}}{V_{1}^{2}}=P_{2}$$

Multiply both sides of the equation by V_{1}^{2}.

$$P_{1}V_{2}^{2}=P_{2}V_{1}^{2}$$

The equation is in standard form.

$$V_{2}^{2}P_{1}=P_{2}V_{1}^{2}$$

Divide both sides by V_{2}^{2}.

$$\frac{V_{2}^{2}P_{1}}{V_{2}^{2}}=\frac{P_{2}V_{1}^{2}}{V_{2}^{2}}$$

Dividing by V_{2}^{2} undoes the multiplication by V_{2}^{2}.

$$P_{1}=\frac{P_{2}V_{1}^{2}}{V_{2}^{2}}$$

Variable P_{1} cannot be equal to 0.

$$P_{1}=\frac{P_{2}V_{1}^{2}}{V_{2}^{2}}\text{, }P_{1}\neq 0$$

Solve for P_2

$$P_{2}=\left(\frac{V_{2}}{V_{1}}\right)^{2}P_{1}$$

$$P_{1}\neq 0\text{ and }V_{1}\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{P_{1}}P_{2}=\frac{V_{2}^{2}}{V_{1}^{2}}$$

Divide both sides by P_{1}^{-1}.

$$\frac{\frac{1}{P_{1}}P_{2}P_{1}}{1}=\frac{V_{2}^{2}}{V_{1}^{2}\times \frac{1}{P_{1}}}$$

Dividing by P_{1}^{-1} undoes the multiplication by P_{1}^{-1}.

$$P_{2}=\frac{V_{2}^{2}}{V_{1}^{2}\times \frac{1}{P_{1}}}$$

Divide \frac{V_{2}^{2}}{V_{1}^{2}} by P_{1}^{-1}.

$$P_{2}=\frac{P_{1}V_{2}^{2}}{V_{1}^{2}}$$