How to solve this equation: $\frac{\sqrt[5]{x^3 \sqrt{x\sqrt[3]{x^{-2}}}}}{\sqrt[4]{x\sqrt[3]{x}}}=3$ Please, help me to solve this equation:
$$\frac{\sqrt[5]{x^3\sqrt{x\sqrt[3]{x^{-2}}}}}{\sqrt[4]{x\sqrt[3]{x}}}=3$$
I tried to shorten fraction, but I get very weird numbers like 
$$\frac{\sqrt[30]{x^{19}}}{\sqrt[3]{x}}=3,$$ and I'm stuck there :(

You're almost done. Note that $\frac{1}{x} = x^{-1}$, so 
$$\frac{\sqrt[30]{x^{19}}}{\sqrt[3]{x}} = \sqrt[30]{x^{19}}(\sqrt[3]{x})^{-1} = x^{19/30}x^{-1/3} = x^{9/30}$$
So then
$$x^{9/30} = 3 \quad \Longleftrightarrow \quad x = 3^{30/9} = 3^{10/3} = \sqrt[3]{3^{10}}$$
