\(\displaystyle \L .4k^{\frac{1}{3}} = .1k\)
multiply both sides by 10 to clear the decimals ...
\(\displaystyle \L 4k^{\frac{1}{3}} = k\)
cube both sides ...
\(\displaystyle \L 64k = k^3\)
move all terms to one side and set = 0 ...
\(\displaystyle \L 0 = k^3 - 64k\)
factor, step 1 ...
\(\displaystyle \L 0 = k(k^2 - 64)\)
factor, step 2 ...
\(\displaystyle \L 0 = k(k + 8)(k - 8)\)
as it turns out, you get three valid solutions for k ...
k = 0, k = -8, and k = 8.