To simplify the expression \( 136 \cdot 13 - 12 \), we can factor it or rewrite it in a different form. Let's analyze the options given:
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13112: This seems like a numerical value and does not represent the expression.
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13 superscript \( \frac{11}{2} \): This is another form and would need verification.
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13−3: This is not equivalent as well.
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13 superscript negative 3: This equals to \( \frac{1}{13^3} \), which also does not match.
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1133: This denotes \( \frac{1}{13^3} \).
Now, let's analyze the expression by calculating:
- \( 136 \cdot 13 = 1768 \)
- \( 1768 - 12 = 1756 \)
Now let's see if we can find an equivalent expression:
Since by direct substitution, none of these options seems to directly equal to \( 1756 \), we might have to examine depending on more context that might have been missed regarding simplification or factoring methods.
If simplifying \( 136 - \frac{12}{13} \) could lead us towards factoring related to this result directly or using logarithmic forms or exponents might eventually help, but based on the above numeric findings, the output does not simplify directly using algebraic methods directly from what is provided on the prompt.
Thus, without further context or another method of simplification to link back to the results, an equivalent form cannot be definitely established among the options provided.
Would you like to approach this differently or provide additional context?