Answer :
The radical expressions which are equivalent to the number 5²/³ are (∛5)² and ∛(5²). Option 3 and 6 are correct.
What is the equivalent expression?
Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
It has to select all radical expressions that are equivalent to 5²/³. Let the radical expression which is equivalent to the number 5²/³ is n. Thus,
[tex]n=5^\dfrac{2}{3}\\[/tex]
Here, the number written in the numberator of the power should be written as the power of the number and number written in the denominator should be written as the root iof the number.
Rewrite the above expression as,
[tex]n=(\sqrt[3]{5})^2[/tex]
Thus the option 6 is correct. It can also be written as,
[tex]n=\sqrt[3]{5^2}[/tex]
Thus the option 3 is also correct. Hence, the radical expressions which are equivalent to the number 5²/³ are (∛5)² and ∛(5²).
Learn more about the equivalent expression here;
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