Answer:
D. The sixth root of three
Step-by-step explanation:
Translate from words to math symbols:
three to the one third power all over three to the one sixth power
[tex]\frac{3^{\frac{1}{3} } }{3^{\frac{1}{6} } } \\[/tex]
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:
[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} }[/tex]
Simplify:
[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} } = \frac{\sqrt[3]{3} }{\sqrt[6]{3} } * \frac{\sqrt[6]{3^{5} } }{\sqrt[6]{3^{5} } } = \frac{\sqrt[3]{3} *\sqrt[6]{3^{5} } }{\sqrt[6]{3^{6} } } = \frac{3^{\frac{1}{3} }*3^{\frac{5}{6} } }{3^{\frac{6}{6} } } = \frac{3^{(\frac{1}{3} +\frac{5}{6} )} }{3} = \frac{3^{(\frac{2}{6} +\frac{5}{6} )} }{3} = \frac{3^{\frac{7}{6} } }{3} = \frac{3^{\frac{1}{6} } *3}{3} = \\\\3^{\frac{1}{6} } = \sqrt[6]{3}[/tex]
Answer:
[tex]\sqrt[6]{3}[/tex]
D. the sixth root of three
