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

1 answer

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 \( 3^{1} \cdot 6^4 \).