Question

What is 3^√54
simplified?

Note: You will find the option to add a cubic root symbol in the Algebra ( ×
) keyboard.

Answer 1

To simplify \( 3^{\sqrt{54}} \), we first simplify \(\sqrt{54}\):

\[
\sqrt{54} = \sqrt{9 \cdot 6} = \sqrt{9} \cdot \sqrt{6} = 3\sqrt{6}
\]

Now we can rewrite \( 3^{\sqrt{54}} \):

\[
3^{\sqrt{54}} = 3^{3\sqrt{6}} = (3^3)^{\sqrt{6}} = 27^{\sqrt{6}}
\]

Thus, the simplified form of \( 3^{\sqrt{54}} \) is:

\[
27^{\sqrt{6}}
\]