Answer:
A and C
Step-by-step explanation:
Rewriting for the sake of clarity:
Select all radical expressions that are equivalent to [tex]3^{\frac{4}{7}}[/tex]
[tex]a)(\sqrt[7]{3^{4}})\\b)\sqrt[4]{21}\\c)\sqrt[7]{81}\\d)\sqrt[4]{3^{7}}\\e)\sqrt[7]{12}\\f)\sqrt[4]{3^{7}}[/tex]
1) According to the Exponents Law, when we have a fraction as an exponent the numerator of it will be the radicand's exponent and the denominator will be the index of it.
[tex]3^{\frac{4}{7}}=(\sqrt[7]{3^{4}})[/tex]
2) We can raise the 3 to the 4th power. And rewrite the radicand as the result of that:
[tex]3^{\frac{4}{7}}=\sqrt[7]{3^{4}}=\sqrt[4]{21}[/tex]
