X* x^1/6-63*x^1/6*x^1/3-64x^-1/6=0решите уравнение.прошу подробное объяснение ,высокая...

Решите задачу:

$x\cdot x^\frac{1}{6}-63x^\frac{1}{6}\cdot x^\frac{1}{3}-\frac{64}{x^\frac{1}{6}}=0\\\\x^\frac{7}{6}-63x^\frac{3}{6}-\frac{64}{x^\frac{1}{6}}=0\\\\x^\frac{3}{6}(x^\frac{4}{6}-63-64x^{-\frac{4}{6}})=0\\\\x^\frac{1}{2}(x^\frac{2}{3}-63-64x^{-\frac{2}{3}})=0\\x^\frac{1}{2}=0\;\to x=0\\t=x^\frac{2}{3},\;\;t-63-\frac{64}{t}=0\\t^2-63t-64=0\\t_1=-1,\;\;t_2=64\\x^\frac{2}{3}=64,\;x=64^\frac{3}{2}=\sqrt{64^3}=8^3=512\\x^\frac{2}{3}=-1,\;\;x=(-1)^\frac{3}{2}=\sqrt{(-1)^3}=\sqrt{-1}\;\; ne \;syshestvyet$