Solve {l}{k=3}{l={(3^{k}+6^k+6^k+3^k)}^frac{1{k}}}{text{Solvefor}mtext{where}}{m=l}

$$\left. \begin{array} { l } { k = 3 }\\ { l = {(3 ^ {k} + 6 ^ {k} + 6 ^ {k} + 3 ^ {k})} ^ {\frac{1}{k}} }\\ { \text{Solve for } m \text{ where} } \\ { m = l } \end{array} \right.$$

Solve for k, l, m

$$m=3\sqrt[3]{18}\approx 7.862224183$$

Solution Steps

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

$$l=\left(3^{3}+6^{3}+6^{3}+3^{3}\right)^{\frac{1}{3}}$$

Calculate 3 to the power of 3 and get 27.

$$l=\left(27+6^{3}+6^{3}+3^{3}\right)^{\frac{1}{3}}$$

Calculate 6 to the power of 3 and get 216.

$$l=\left(27+216+6^{3}+3^{3}\right)^{\frac{1}{3}}$$

Add 27 and 216 to get 243.

$$l=\left(243+6^{3}+3^{3}\right)^{\frac{1}{3}}$$

Calculate 6 to the power of 3 and get 216.

$$l=\left(243+216+3^{3}\right)^{\frac{1}{3}}$$

Add 243 and 216 to get 459.

$$l=\left(459+3^{3}\right)^{\frac{1}{3}}$$

Calculate 3 to the power of 3 and get 27.

$$l=\left(459+27\right)^{\frac{1}{3}}$$

Add 459 and 27 to get 486.

$$l=486^{\frac{1}{3}}$$

Reorder the terms.

$$l=\sqrt[3]{486}$$

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

$$m=\sqrt[3]{486}$$

The system is now solved.

$$k=3 l=\sqrt[3]{486} m=\sqrt[3]{486}$$