Answer:
Option A and C.
Step-by-step explanation:
Consider the below figure attached with this question.
The given expression is
[tex]3^{\frac{4}{7}}[/tex]
The properties of exponent:
[tex](a^m)^n=a^{mn}[/tex]
[tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]
Using these properties simplify all expression.
[tex](\sqrt[7]{3})^4=(3^{\frac{1}{7}})^4=3^{\frac{4}{7}}[/tex]
[tex]\sqrt[4]{21}=21^{\frac{1}{4}}\neq 3^{\frac{4}{7}}[/tex]
[tex]\sqrt[7]{81}=\sqrt[7]{3^4}=(3^4)^{\frac{1}{7}}=3^{\frac{4}{7}}[/tex]
[tex]\sqrt[4]{3^7}=(3^7)^{\frac{1}{4}}=3^{\frac{7}{4}}\neq 3^{\frac{4}{7}}[/tex]
[tex]\sqrt[7]{12}=12^{\frac{1}{7}}\neq 3^{\frac{4}{7}}[/tex]
[tex](\sqrt[4]{3})^7=(3^{\frac{1}{4}})^7=3^{\frac{7}{4}}\neq 3^{\frac{4}{7}}[/tex]
Therefore, the correct options are A and C.
