To evaluate \(\left(\frac{8}{9}\right)^2\), we square both the numerator and the denominator:
\[ \left(\frac{8}{9}\right)^2 = \frac{8^2}{9^2} \]
Calculating \(8^2\) and \(9^2\):
\[ 8^2 = 64 \]
\[ 9^2 = 81 \]
Therefore, we have:
\[ \left(\frac{8}{9}\right)^2 = \frac{64}{81} \]
Now, we want to express \(\frac{64}{81}\) in simplest form. Since 64 and 81 have no common factors (64 is \(2^6\) and 81 is \(3^4\)), the fraction \(\frac{64}{81}\) is already in simplest form.
Thus, the final answer is:
\[ \frac{64}{81} \]
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