Answer:
A and C
Step-by-step explanation:
Using the rule of exponents
[tex](a^m)^{n}[/tex] ⇔ [tex]a^{mn}[/tex]
Using the rule of radicals
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]
Given
([tex]2^{\frac{1}{6} }[/tex] )^9
= [tex]2^{\frac{3}{2} }[/tex]
= [tex]\sqrt{2^{3} }[/tex] = [tex]\sqrt{8}[/tex] → A
and
= [tex]\sqrt[6]{2^{9} }[/tex] = [tex]\sqrt[6]{512}[/tex] → C
