The product of the numbers \(10 \times 4 \times 3 \times 3 \times 3 \times 3 \times 4\) can be calculated step by step:
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First, multiply the constant numbers: \[ 4 \times 4 = 16 \]
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Then multiply the 3s: \[ 3 \times 3 = 9 \] \[ 9 \times 3 = 27 \] \[ 27 \times 3 = 81 \]
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Now multiply everything together: \[ 10 \times 16 \times 81 \]
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First, calculate \(10 \times 16\): \[ 10 \times 16 = 160 \]
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Finally, multiply \(160 \times 81\): \[ 160 \times 81 = 12960 \]
Thus, the final result is: \[ \boxed{12960} \]