Solve n/y^2=5y

$$\frac { n } { y ^ { 2 } } = 5 y$$

Solve for n

$$n=5y^{3}$$

$$y\neq 0$$

Solution Steps

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

$$n=5yy^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$n=5y^{3}$$

Solve for y (complex solution)

$$y=\frac{5^{\frac{2}{3}}e^{\frac{2\pi i}{3}}\sqrt[3]{n}}{5}$$

$$y=\frac{5^{\frac{2}{3}}\sqrt[3]{n}}{5}$$

$$y=\frac{5^{\frac{2}{3}}e^{\frac{4\pi i}{3}}\sqrt[3]{n}}{5}\text{, }n\neq 0$$

Solve for y

$$y=\frac{5^{\frac{2}{3}}\sqrt[3]{n}}{5}$$

$$n\neq 0$$