Question

2 x 10^2 =














Question
A student simplified this expression:  33⋅3−2(36)2
using these steps:

Step 1:   3−6312


Step 2:   136⋅312


Step 3:   1318


Which of these steps contains a mistake from the previous step?

(1 point)
Responses

There are no mistakes.  The answer is correct.
There are no mistakes.  The answer is correct.

Step 1 had the mistake.  Correct answer to this step is 31312
Step 1 had the mistake.  Correct answer to this step is the fraction with numerator 3 to the 1th power and denominator 3 to the 12th power

Step 2 had the mistake.  Correct answer to this step is 36
Step 2 had the mistake.  Correct answer to this step is 3 to the 6th power

Step 3 had the mistake.  Correct answer to this step is 136

Answer 1

Let's analyze the student's steps to find the mistake.

The original expression is \( 33 \cdot 3^{-2} \cdot (36)^2 \).

Let's simplify it step by step:

1. Begin with the original expression:
\[
33 \cdot 3^{-2} \cdot (36)^2
\]

2. Recognize \( 36 = 6^2 \), so:
\[
(36)^2 = 36^2 = (6^2)^2 = 6^4
\]

Now we note that \( 33 = 3^3 \):
\[
3^3 \cdot 3^{-2} \cdot 6^4
\]

3. Combine the powers of 3:
\[
3^{3 - 2} = 3^1 = 3
\]

Thus, we now have:
\[
3 \cdot 6^4
\]

4. Using the value of \( 6 \) and simplifying we get:
\[
6^4 = (2 \cdot 3)^4 = 2^4 \cdot 3^4 = 16 \cdot 81 = 1296
\]

5. Now substitute back to find:
\[
\( 3 \cdot 1296 = 3888
\]

Now, let’s go through the steps provided by the student:

**Step 1**: Claim was:
\[
3^{-6} \cdot 3^{12}
\]
This seems to be simplifying incorrectly, since the initial terms should simplify to \( 3^{3-2} \), not this combination.

**Step 2**: Claims:
\[
1^3 \cdot 3^{12}
\]
This is also incorrect as it doesn't follow logically from the first step.

**Step 3**: Claims:
\[
1^3/8
\]
Again not correct as it doesn't follow the required calculations.

Based on these observations:

- The first step (Step 1) contains a mistake. The correct simplification for Step 1 should have been \( 3^{3-2} \cdot 6^4 \) instead.

So the response would be: **Step 1 had the mistake. Correct answer to this step is \( 3^{1} \cdot 6^4 \)**.