To evaluate \((\frac{2}{3})^4\), we raise both the numerator and the denominator to the 4th power.
\[ \left(\frac{2}{3}\right)^4 = \frac{2^4}{3^4} \]
Calculating \(2^4\):
\[ 2^4 = 16 \]
Calculating \(3^4\):
\[ 3^4 = 81 \]
Now we can combine these results:
\[ \left(\frac{2}{3}\right)^4 = \frac{16}{81} \]
Since 16 and 81 have no common factors (16 is \(2^4\) and 81 is \(3^4\)), the fraction \(\frac{16}{81}\) is already in simplest form.
Thus, the final answer is:
\[ \frac{16}{81} \]
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