Let's simplify the expression step by step, following the order of operations.
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Start with the original expression: \( 3 \times 4^2 - 9 \times 2 \).
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Evaluate the exponent: \( 4^2 = 16 \). So, the expression becomes: \( 3 \times 16 - 9 \times 2 \).
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Perform the multiplications:
- \( 3 \times 16 = 48 \)
- \( 9 \times 2 = 18 \)
Now, we have: \( 48 - 18 \).
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Finally, subtract: \( 48 - 18 = 30 \).
So the final simplified result is: \[ \boxed{30} \]