Solve x^16=5/y

$$x ^ { 16 } = \frac { 5 } { y }$$

Solve for y

$$y=\frac{5}{x^{16}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$yx^{16}=5$$

The equation is in standard form.

$$x^{16}y=5$$

Divide both sides by x^{16}.

$$\frac{x^{16}y}{x^{16}}=\frac{5}{x^{16}}$$

Dividing by x^{16} undoes the multiplication by x^{16}.

$$y=\frac{5}{x^{16}}$$

Variable y cannot be equal to 0.

$$y=\frac{5}{x^{16}}\text{, }y\neq 0$$

Solve for x (complex solution)

$$x\in \sqrt[16]{5}e^{\frac{\pi i}{8}}y^{-\frac{1}{16}},\sqrt[16]{5}y^{-\frac{1}{16}},\sqrt{2}\sqrt[16]{5}\left(\frac{1}{2}+\frac{1}{2}i\right)y^{-\frac{1}{16}},\sqrt[16]{5}e^{\frac{3\pi i}{8}}y^{-\frac{1}{16}},\sqrt[16]{5}iy^{-\frac{1}{16}},\sqrt[16]{5}e^{\frac{5\pi i}{8}}y^{-\frac{1}{16}},\sqrt{2}\sqrt[16]{5}\left(-\frac{1}{2}+\frac{1}{2}i\right)y^{-\frac{1}{16}},\sqrt[16]{5}e^{\frac{7\pi i}{8}}y^{-\frac{1}{16}},-\sqrt[16]{5}y^{-\frac{1}{16}},\sqrt[16]{5}e^{\frac{9\pi i}{8}}y^{-\frac{1}{16}},\sqrt{2}\sqrt[16]{5}\left(-\frac{1}{2}-\frac{1}{2}i\right)y^{-\frac{1}{16}},\sqrt[16]{5}e^{\frac{11\pi i}{8}}y^{-\frac{1}{16}},-\sqrt[16]{5}iy^{-\frac{1}{16}},\sqrt[16]{5}e^{\frac{13\pi i}{8}}y^{-\frac{1}{16}},\sqrt{2}\sqrt[16]{5}\left(\frac{1}{2}-\frac{1}{2}i\right)y^{-\frac{1}{16}},\sqrt[16]{5}e^{\frac{15\pi i}{8}}y^{-\frac{1}{16}}$$

$$y\neq 0$$

Solve for x

$$x=\sqrt[16]{\frac{5}{y}}$$

$$x=-\sqrt[16]{\frac{5}{y}}\text{, }y>0$$