Solve z=(4y/x)^-1

$$z = ( \frac { 4 y } { x } ) ^ { - 1 }$$

Solve for x

$$x=4yz$$

$$z\neq 0\text{ and }y\neq 0$$

Solution Steps

To raise \frac{4y}{x} to a power, raise both numerator and denominator to the power and then divide.

$$z=\frac{\left(4y\right)^{-1}}{x^{-1}}$$

Expand \left(4y\right)^{-1}.

$$z=\frac{4^{-1}y^{-1}}{x^{-1}}$$

Calculate 4 to the power of -1 and get \frac{1}{4}.

$$z=\frac{\frac{1}{4}y^{-1}}{x^{-1}}$$

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

$$\frac{\frac{1}{4}y^{-1}}{x^{-1}}=z$$

Reorder the terms.

$$\frac{\frac{1}{4}\times \frac{1}{y}x}{1}=z$$

Multiply \frac{1}{4} times \frac{1}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{4y}x}{1}=z$$

Express \frac{1}{4y}x as a single fraction.

$$\frac{\frac{x}{4y}}{1}=z$$

Anything divided by one gives itself.

$$\frac{x}{4y}=z$$

Multiply both sides of the equation by 4y.

$$x=z\times 4y$$

Reorder the terms.

$$x=4yz$$

Solve for y

$$y=\frac{x}{4z}$$

$$x\neq 0\text{ and }z\neq 0$$

Steps for Solving Linear Equation

To raise \frac{4y}{x} to a power, raise both numerator and denominator to the power and then divide.

$$z=\frac{\left(4y\right)^{-1}}{x^{-1}}$$

Expand \left(4y\right)^{-1}.

$$z=\frac{4^{-1}y^{-1}}{x^{-1}}$$

Calculate 4 to the power of -1 and get \frac{1}{4}.

$$z=\frac{\frac{1}{4}y^{-1}}{x^{-1}}$$

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

$$\frac{\frac{1}{4}y^{-1}}{x^{-1}}=z$$

Reorder the terms.

$$\frac{\frac{1}{4}\times \frac{1}{y}x}{1}=z$$

Multiply \frac{1}{4} times \frac{1}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{4y}x}{1}=z$$

Express \frac{1}{4y}x as a single fraction.

$$\frac{\frac{x}{4y}}{1}=z$$

Anything divided by one gives itself.

$$\frac{x}{4y}=z$$

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4y.

$$x=z\times 4y$$

Reorder the terms.

$$x=4yz$$

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

$$4yz=x$$

The equation is in standard form.

$$4zy=x$$

Divide both sides by 4z.

$$\frac{4zy}{4z}=\frac{x}{4z}$$

Dividing by 4z undoes the multiplication by 4z.

$$y=\frac{x}{4z}$$

Variable y cannot be equal to 0.

$$y=\frac{x}{4z}\text{, }y\neq 0$$