We have the following:
I)
[tex]\sqrt[n]{a}=a^{\frac{1}{n}}[/tex]
It´s true
II)
[tex]a^{\frac{1}{2}}=\sqrt[]{a}[/tex]
It´s true
III)
[tex]\begin{gathered} a^{\frac{p}{q}}=\sqrt[p]{a^q}=(\sqrt[p]{a})^q \\ (\sqrt[p]{a})^q=(a^{\frac{1}{p}})^q=a^{\frac{q}{p}} \end{gathered}[/tex]
It´s false
IV)
[tex]\sqrt[]{a}[/tex]
It´s true
V)
[tex]\begin{gathered} a^{\frac{1}{n}}=\sqrt[]{a^n} \\ \sqrt[]{a^n}=a^{\frac{n}{2}} \end{gathered}[/tex]
It´s false
