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We can to convert the expression  [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression   [tex]\sqrt[5]{9}[/tex].  by using the laws of indices.

What is a radical expression?

A radical expression is an expression of the form ⁿ√x where it is called the nth root of x.

Now, to write [tex](3^{\frac{1}{5} } )^{2}[/tex] as  the radical expression [tex]\sqrt[5]{9}[/tex], we use following laws of indices

  • The power law of indices. [tex](x^{\frac{1}{b} } )^{a} = (x^{a} )^{\frac{1}{b} }[/tex] and
  • root law of indices [tex]x^{\frac{1}{a} } = \sqrt[a]{x}[/tex]

So,  [tex](3^{\frac{1}{5} } )^{2} = (3^{2} )^{\frac{1}{5} }[/tex]

  [tex](3^{2} )^{\frac{1}{5} } = 9^{\frac{1}{5} } = \sqrt[5]{9}[/tex]

Thus, we can to convert the expression  [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression   [tex]\sqrt[5]{9}[/tex].  by using the laws of indices.

Learn more about radical expression here:

https://brainly.com/question/3005248

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