[color=#0000ff][b]Cube root of [i]x[/i] [/b]means the number, for which[/color][br][br] [math]\Large \textcolor{blue}{(\sqrt[3] x)^3=x.}[/math][br][br] [br]Also with cube root:[br][br] 1.  [math]\large \textcolor{blue}{\sqrt[3]{ab}=\sqrt[3] a\sqrt[3] b}[/math][br][br] [br] 2.  [math]\large \textcolor{blue}{\sqrt[3]\frac a b=\frac \sqrt[3] a \sqrt[3] b\;\;\; b>0}[/math][br] [br][br] [br][color=#0000ff]Examples:[/color][br][br]  1.  [math]\large \sqrt[3] 8=\sqrt[3]{2^3}=2[/math][br] [br]  2.  [math]\large \sqrt[3] {-8}=\sqrt[3]{(-2)^3}=-2[/math][br] [br][br][color=#0000ff]Example 3. [br][/color][br][math]\large\sqrt[3]{27a^2b^3c^4}=\sqrt[3]{27}\cdot \sqrt[3]{a^2}\cdot \sqrt[3]{b^3}\cdot \sqrt[3]{c^4}=\sqrt[3] {3^3}\cdot\sqrt[3]{a^2}\cdot\sqrt[3]{b^3}\cdot\sqrt[3]{c^3\cdot c}=3bc\cdot\sqrt[3]{a^2c}[/math][br][br][br][color=#0000ff]Example 4. [math]\large \sqrt[3]\frac{16a^3b^5}{c^6}=\frac \sqrt[3]{16a^3b^5} \sqrt[3]{c^6}=\frac \sqrt[3]{2^3\cdot 2a^3b^3b^2} \sqrt[3]{(c^2)^3}=\frac{2ab\sqrt[3]{2b^2}}{c^2}[/math][br][br][/color][br][br][color=#0000ff]Example 5. [/color][br][br]  [math]\large \frac {\sqrt[3]{a^2b}-\sqrt[3]{ab^2}}{\sqrt[3]{ab}}=\frac \sqrt[3]{a^2b}\sqrt[3]{ab}-\frac \sqrt[3]{ab^2}\sqrt[3]{ab}=\sqrt[3]{\frac{a^2b}{ab}}-\sqrt[3]{\frac{ab^2}{ab}}=\sqrt[3]{a}-\sqrt[3]{b}[/math][br][br] [br]