Consider the property,
[tex](x^m)^n=(x^n)^m=x^{mn}^{}[/tex]
(a)
Consider the given expression,
[tex]\sqrt[]{w^{16}}[/tex]
Simplify the given expression as,
[tex]\begin{gathered} \sqrt[]{w^{16}}=(w^{16})^{\frac{1}{2}}=w^{16\times\frac{1}{2}}=w^8 \\ \Rightarrow\sqrt[]{w^{16}}=\lvert w^8\rvert \end{gathered}[/tex]
(b)
Consider the given expression,
[tex]\sqrt[]{w^{14}}[/tex]
Simplify the given expression as,
[tex]\begin{gathered} \sqrt[]{w^{14}}=(w^{14})^{\frac{1}{2}}=w^{14\times\frac{1}{2}}=w^7 \\ \Rightarrow\sqrt[]{w^{14}}=\lvert w^7\rvert \end{gathered}[/tex]
