Solve 80f(x)=sqrt[3]{x}

$$80 f ( x ) = \sqrt[ 3 ] { x }$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\frac{x^{-\frac{2}{3}}}{80}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$80xf=\sqrt[3]{x}$$

Divide both sides by 80x.

$$\frac{80xf}{80x}=\frac{\sqrt[3]{x}}{80x}$$

Dividing by 80x undoes the multiplication by 80x.

$$f=\frac{\sqrt[3]{x}}{80x}$$

Divide \sqrt[3]{x} by 80x.

$$f=\frac{x^{-\frac{2}{3}}}{80}$$

Solve for f

$$\left\{\begin{matrix}f=\frac{1}{80x^{\frac{2}{3}}}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$80xf=\sqrt[3]{x}$$

Divide both sides by 80x.

$$\frac{80xf}{80x}=\frac{\sqrt[3]{x}}{80x}$$

Dividing by 80x undoes the multiplication by 80x.

$$f=\frac{\sqrt[3]{x}}{80x}$$

Divide \sqrt[3]{x} by 80x.

$$f=\frac{1}{80x^{\frac{2}{3}}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{\sqrt{5}f^{-\frac{3}{2}}}{1600}\text{, }&arg(f^{-\frac{1}{2}})<\frac{2\pi }{3}\text{ and }f\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\frac{\sqrt{5}}{1600f^{\frac{3}{2}}}\text{; }x=\frac{\sqrt{5}}{1600f^{\frac{3}{2}}}\text{, }&f>0\end{matrix}\right.$$