True or false√3^(3√2) =(108)^1/6

Question

asked May 18, 2023 163k views

1 Answer

JDawwgy · Answer 1 · 2023-05-25T14:20:32+0000

Answer:

False

Explanations:

For the Left Hand side of the expression:

$\sqrt[]{3}^{(3\sqrt[]{2})}$

This can be simplified as:

$\begin{gathered} 3^{(1)/(2)(3\sqrt[]{2})} \\ =3^{1.5\sqrt[]{2}} \\ =3^(2.12) \\ =\text{ }10.27 \end{gathered}$

For the Right Hand Side of the expression:

$\begin{gathered} (108)^{(1)/(6)} \\ =(108)^(0.167) \\ =\text{ }2.19 \end{gathered}$

Since the Left Hand Side does not equal the Right Hand Side after simplification, the expression is not true