To simplify the expression \((9^{2/3})^{3/4}\), we can use the property of exponents which states that \((a^m)^n = a^{m \cdot n}\).
Let's break it down step-by-step:
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Apply the exponent multiplication rule:
\[ (9^{2/3})^{3/4} = 9^{(2/3) \cdot (3/4)} \]
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Multiply the exponents:
\[ \frac{2}{3} \cdot \frac{3}{4} = \frac{2 \cdot 3}{3 \cdot 4} = \frac{6}{12} = \frac{1}{2} \]
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Now rewrite the expression:
\[ 9^{(2/3) \cdot (3/4)} = 9^{1/2} \]
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Evaluate \(9^{1/2}\):
\(9^{1/2}\) is the square root of 9, which is 3.
Therefore, the simplified expression is:
\[ \boxed{3} \]