Question

Can someone please explain how ormula1" title="(3^{\frac{1}{5} } )^{2}" alt="(3^{\frac{1}{5} } )^{2}" align="absmiddle" class="latex-formula"> can be written as the radical expression $\sqrt[5]{9}$ ???

Answer 1

We can to convert the expression  $(3^{\frac{1}{5} } )^{2}$ to the radical expression   $\sqrt[5]{9}$.  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 $(3^{\frac{1}{5} } )^{2}$ as  the radical expression $\sqrt[5]{9}$, we use following laws of indices

• The power law of indices. $(x^{\frac{1}{b} } )^{a} = (x^{a} )^{\frac{1}{b} }$ and

• root law of indices $x^{\frac{1}{a} } = \sqrt[a]{x}$

So,  $(3^{\frac{1}{5} } )^{2} = (3^{2} )^{\frac{1}{5} }$

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

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

Learn more about radical expression here:

brainly.com/question/3005248

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