To determine the validity of the equation \((3\sqrt{4})^{24}/(\sqrt{3})^{6}=(4/3)^{5}\), let's simplify both sides step by step.
**Left Side:**
\[
\frac{(3\sqrt{4})^{24}}{(\sqrt{3})^{6}}
\]
1. Simplify \( \sqrt{4} \):
\[
\sqrt{4} = 2
\]
So \( (3\sqrt{4})^{24} = (3 \cdot 2)^{24} = (6)^{24} \).
2. Now for the denominator:
\[
(\sqrt{3})^{6} = (3^{1/2})^{6} = 3^{6/2} = 3^{3} = 27
\]
3. Now, rewrite the left side:
\[
\frac{(6)^{24}}{27} = \frac{6^{24}}{3^{3}} = 6^{24} \cdot 3^{-3}
\]
**Right Side:**
\[
\left(\frac{4}{3}\right)^{5} = \frac{4^5}{3^5}
\]
**Comparison:**
To simplify further we can express \(6^{24}\):
\[
6^{24} = (2 \cdot 3)^{24} = 2^{24} \cdot 3^{24}
\]
Then substituting that in:
\[
6^{24} \cdot 3^{-3} = 2^{24} \cdot 3^{21}
\]
Now let's simplify the right side:
\[
\frac{4^5}{3^5} = \frac{(2^2)^5}{3^5} = \frac{2^{10}}{3^5}
\]
**Final Comparison:**
\[
2^{24} \cdot 3^{21} \text{ (left side) } \quad \text{and } \quad \frac{2^{10}}{3^5} = 2^{10} \cdot 3^{-5} \text{ (right side)}
\]
The powers of 2 and 3 on both sides are thus:
- Left side: \(2^{24}\) and \(3^{21}\)
- Right side: \(2^{10}\) and \(3^{-5}\).
Since these powers do not match, we can conclude:
The equation is **False**. The Power of a Power Property has not been applied correctly.
Thus, the correct response is:
**False. The Power of a Power Property has not been applied correctly.**