Answer:
4. I, II and III
Step-by-step explanation:
Hope it helps you in your learning process.
I.
[tex]\huge\frac{\sqrt[6]{x}}{\sqrt[3]{x}}[/tex]
[tex]\huge=\frac{x^{\frac{1}{6}}}{x^{\frac{1}{3}}}[/tex]
[tex]\huge=\frac{1}{x^{\frac{1}{3}-\frac{1}{6}} }[/tex]
[tex]\huge=\frac{1}{x^{\frac{2}{6}-\frac{1}{6}} }[/tex]
[tex]\huge=\frac{1}{x^{\frac{2-1}{6}} }[/tex]
[tex]\huge=\frac{1}{x^{\frac{1}{6}} }[/tex]
II.
[tex]\huge\frac{x^{\frac{1}{6}}}{x^{\frac{1}{3}}}[/tex]
[tex]\huge=\frac{1}{x^{\frac{1}{3}-\frac{1}{6}} }[/tex]
[tex]\huge=\frac{1}{x^{\frac{2}{6}-\frac{1}{6}} }[/tex]
[tex]\huge=\frac{1}{x^{\frac{2-1}{6}} }[/tex]
[tex]\huge=\frac{1}{x^{\frac{1}{6}} }[/tex]
III
[tex]\huge x^{-\frac{1}{6}}[/tex]
[tex]\huge=\frac{1}{x^{\frac{1}{6}} }[/tex]
