[tex] \text{Use:}\\\sqrt[n]{a^n}=a\\\\a^\frac{m}{n}=\sqrt[n]{a^m}\\\\(a^n)^m=a^{n\cdot m}\\\\a^n\cdot a^m=a^{n+m}\\\\1.\ \sqrt[3]{-512}=\sqrt[3]{(-8)^3}=-8\\\\2.\ \sqrt[4]{4096}=\sqrt[4]{8^4}=8\\\\3.\ 343^\frac{1}{3}=(7^3)^\frac{1}{3}=7^{3\cdot\frac{1}{3}}=7^1=7\\\\4.\ \sqrt[6]{x^{16}}=(x^{16})^\frac{1}{6}=x^{16\cdot\frac{1}{6}}=x^{8\cdot\frac{1}{3}}=x^\frac{8}{3}=x^{2\frac{2}{3}}=x^{2+\frac{2}{3}}=x^2x^\frac{2}{3}=x^2\sqrt[3]{x^2} [/tex]
[tex] 2+\sqrt[3]{5x+2}=10\ \ \ \ |-2\\\\\sqrt[3]{5x+2}=8\ \ \ \ |^3\\\\(\sqrt[3]{5x+2})^3=8^3\\\\5x+2=512\ \ \ \ |-2\\\\5x=510\ \ \ \ |:5\\\\x=102 [/tex]
