Let's break down the original expression step by step to identify any mistakes.
The original expression is: \[ 33 \cdot 3^{-2}(36)^2 \]
We will execute the steps provided and check for errors.
Step 1: Simplifying \( 33 \cdot 3^{-2}(36)^2 \)
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First, simplify \( (36)^2 \): \[ (36)^2 = 1296 \]
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Now, express the original expression: \[ 33 \cdot 3^{-2} \cdot 1296 \]
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Evaluate \( 3^{-2} \): \[ 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \]
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Now combine: \[ 33 \cdot \frac{1}{9} \cdot 1296 = \frac{33 \cdot 1296}{9} \]
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Calculate \( \frac{33 \cdot 1296}{9} \): \( 33 \cdot 1296 = 42816 \), Now divide: \[ \frac{42816}{9} = 4756 \]
So, from the calculations, step 1 simplifies correctly to: \[ \frac{33 \cdot 1296}{9} \]
The student's Step 1 results in \( 3^{-6} 3^{12} \), which appears incorrect.
Step 2:
The student then presents \( 136 \cdot 3^{12} \) in Step 2.
If we properly analyze step 2: Based on the simplified product from step 1: We should be simplifying \( \frac{33 \cdot 1296}{9} \).
Conclusion:
There was a mistake in Step 1. The expression should have been simplified to: \[ \frac{33}{9} \cdot 1296 \] which can be further simplified.
So the correct answer is that Step 1 had the mistake. The correct answer for this step is actually \( 31^{12} \) or similar structures, not the initial misunderstanding in combining powers that they showed.
Therefore the correct response is: Step 1 had the mistake. Correct answer to this step is the fraction with numerator \( 3^1 \) to the power and denominator \( 3^{12} \).