Question
simplify
3^√24c^16
3^√24c^16
Answers
GPT-4o mini
To simplify the expression \( 3^{\sqrt{24}c^{16}} \), we can start by simplifying \( \sqrt{24} \).
First, factor \( 24 \):
\[
24 = 4 \times 6 = 4 \times 2 \times 3
\]
Now, we find the square root:
\[
\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}
\]
Next, substitute this back into the original expression:
\[
3^{\sqrt{24}c^{16}} = 3^{2\sqrt{6}c^{16}}
\]
This is the simplified form of the expression. Thus, the simplified expression is:
\[
3^{2\sqrt{6}c^{16}}
\]
First, factor \( 24 \):
\[
24 = 4 \times 6 = 4 \times 2 \times 3
\]
Now, we find the square root:
\[
\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}
\]
Next, substitute this back into the original expression:
\[
3^{\sqrt{24}c^{16}} = 3^{2\sqrt{6}c^{16}}
\]
This is the simplified form of the expression. Thus, the simplified expression is:
\[
3^{2\sqrt{6}c^{16}}
\]