Answer:
Option C & D
Step-by-step explanation:
__________________________________________________________
FACTS TO KNOW BEFORE SOLVING :-
Lets say there's an expression [tex]x^{\frac{a}{b} }[/tex] .
It can be also written it as → [tex](\sqrt[b]{x} )^{a}[/tex] and vice-versa.
__________________________________________________________
Lets come to the question.
- In option A , [tex]7^{\frac{5}{7} }[/tex] can be also written as [tex](\sqrt[7]{7} )^{5}[/tex] . But it doesn't match with the other expression given. Hence they are not equivalent expressions.
- In option B , [tex]6^{\frac{2}{7} }[/tex] can be also written as [tex](\sqrt[7]{6} )^{2}[/tex] . But it doesn't match with the other expression given. Hence they are not equivalent expressions.
- In option C , [tex]5^{\frac{3}{2} }[/tex] can be also written as [tex](\sqrt{5} )^{3}[/tex]. Hence they are equivalent expressions.
- In option D , [tex](\sqrt[4]{81} )^{5}[/tex] can be also written as [tex]81^{\frac{5}{4} }[/tex] . Hence they are equivalent expressions
Thus , Option C & D are correct.
