Solve I_{F}:(A)(-2^frac{1{4}})^4=-2

$$I _ { F } : ( A ) ( - 2 ^ { \frac { 1 } { 4 } } ) ^ { 4 } = - 2$$

Solve for A

$$A=-I_{F}$$

$$I_{F}\neq 0$$

Steps for Solving Linear Equation

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

$$I_{F}\left(-2^{\frac{1}{4}}\right)^{4}=-2A$$

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

$$-2A=I_{F}\left(-2^{\frac{1}{4}}\right)^{4}$$

Reorder the terms.

$$-2A=\left(-\sqrt[4]{2}\right)^{4}I_{F}$$

Expand \left(-\sqrt[4]{2}\right)^{4}.

$$-2A=\left(-1\right)^{4}\left(\sqrt[4]{2}\right)^{4}I_{F}$$

Calculate -1 to the power of 4 and get 1.

$$-2A=1\left(\sqrt[4]{2}\right)^{4}I_{F}$$

Reorder the terms.

$$-2A=\left(\sqrt[4]{2}\right)^{4}I_{F}$$

Divide both sides by -2.

$$\frac{-2A}{-2}=\frac{2I_{F}}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$A=\frac{2I_{F}}{-2}$$

Divide 2I_{F} by -2.

$$A=-I_{F}$$

Variable A cannot be equal to 0.

$$A=-I_{F}\text{, }A\neq 0$$

Solve for I_F

$$I_{F}=-A$$

$$A\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by A.

$$I_{F}\left(-2^{\frac{1}{4}}\right)^{4}=-2A$$

Reorder the terms.

$$\left(-\sqrt[4]{2}\right)^{4}I_{F}=-2A$$

Expand \left(-\sqrt[4]{2}\right)^{4}.

$$\left(-1\right)^{4}\left(\sqrt[4]{2}\right)^{4}I_{F}=-2A$$

Calculate -1 to the power of 4 and get 1.

$$1\left(\sqrt[4]{2}\right)^{4}I_{F}=-2A$$

Reorder the terms.

$$\left(\sqrt[4]{2}\right)^{4}I_{F}=-2A$$

Divide both sides by \left(\sqrt[4]{2}\right)^{4}.

$$\frac{\left(\sqrt[4]{2}\right)^{4}I_{F}}{\left(\sqrt[4]{2}\right)^{4}}=-\frac{2A}{\left(\sqrt[4]{2}\right)^{4}}$$

Dividing by \left(\sqrt[4]{2}\right)^{4} undoes the multiplication by \left(\sqrt[4]{2}\right)^{4}.

$$I_{F}=-\frac{2A}{\left(\sqrt[4]{2}\right)^{4}}$$

Divide -2A by \left(\sqrt[4]{2}\right)^{4}.

$$I_{F}=-A$$