Solve {l}{x=[(2y)^2(3y)^3]^frac{1{5}}}{y=1/2}

$$\left\{ \begin{array} { l } { x = [ ( 2 y ) ^ { 2 } ( 3 y ) ^ { 3 } ] ^ { \frac { 1 } { 5 } } } \\ { y = \frac { 1 } { 2 } } \end{array} \right.$$

Solve for x, y

$$x = \frac{2 ^ {\frac{2}{5}} \cdot 3 ^ {\frac{3}{5}}}{2} \approx 1.275424501$$

$$y=\frac{1}{2}=0.5$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$x=\left(\left(2\times \frac{1}{2}\right)^{2}\times \left(3\times \frac{1}{2}\right)^{3}\right)^{\frac{1}{5}}$$

Multiply 2 and \frac{1}{2} to get 1.

$$x=\left(1^{2}\times \left(3\times \frac{1}{2}\right)^{3}\right)^{\frac{1}{5}}$$

Calculate 1 to the power of 2 and get 1.

$$x=\left(1\times \left(3\times \frac{1}{2}\right)^{3}\right)^{\frac{1}{5}}$$

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$x=\left(1\times \left(\frac{3}{2}\right)^{3}\right)^{\frac{1}{5}}$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$x=\left(1\times \frac{27}{8}\right)^{\frac{1}{5}}$$

Multiply 1 and \frac{27}{8} to get \frac{27}{8}.

$$x=\left(\frac{27}{8}\right)^{\frac{1}{5}}$$

Reorder the terms.

$$x=\sqrt[5]{\frac{27}{8}}$$

The system is now solved.

$$x=\sqrt[5]{\frac{27}{8}} y=\frac{1}{2}$$