Consider the given radical,
[tex]\sqrt[]{128}[/tex]
Factorize the number,
[tex]128=2^7[/tex]
Consider the following properties,
[tex]\begin{gathered} a^{m+1}=a^m\times a \\ a^{mn}=(a^m)^n \end{gathered}[/tex]
Then the radical can be simplified as,
[tex]\sqrt[]{128}=\sqrt[]{2^7}=\sqrt[]{2^6\times2}=\sqrt[]{64\times2}=\sqrt[]{64}\times\sqrt[]{2}[/tex]
Thus, the radical is simplified as,
[tex]\sqrt[]{128}=\sqrt[]{64}\times\sqrt[]{2}=8\sqrt[]{2}[/tex]
