`3^2xx2^2div(6^2-9)+1^2=33`

Options

A. `-` and `div`
B. `+` and `xx`
C. `xx` and `div`
D. `+` and -

Explanation

To solve the equation \(3^2 \times 2^2 \div (6^2 - 9) + 1^2 = 33\), we will follow the order of operations (BODMAS/BIDMAS). Let's break it down step by step.

### Step 1: Calculate the powers
First, we calculate the squares:
- \(3^2 = 9\)
- \(2^2 = 4\)
- \(6^2 = 36\)
- \(1^2 = 1\)

So, we can rewrite the equation as:
\[ 9 \times 4 \div (36 - 9) + 1 = 33 \]

### Step 2: Calculate the expression inside the parentheses
Now, we solve the expression inside the parentheses:
\[ 36 - 9 = 27 \]

Now the equation looks like:
\[ 9 \times 4 \div 27 + 1 = 33 \]

### Step 3: Perform the multiplication
Next, we perform the multiplication:
\[ 9 \times 4 = 36 \]

So we have:
\[ 36 \div 27 + 1 = 33 \]

### Step 4: Perform the division
Now we perform the division:
\[ 36 \div 27 = \frac{36}{27} = \frac{4}{3} \quad (\text{after simplifying}) \]

Now the equation becomes:
\[ \frac{4}{3} + 1 = 33 \]

### Step 5: Add the fractions
To add \(\frac{4}{3}\) and \(1\), we convert \(1\) to a fraction:
\[ 1 = \frac{3}{3} \]

So we have:
\[ \frac{4}{3} + \frac{3}{3} = \frac{7}{3} \]

### Step 6: Check if it equals 33
Now we check:
\[ \frac{7}{3} \neq 33 \]

Since this does not equal 33, we need to change the operations as discussed in the video.

### Step 7: Change the operations
We will change the division to subtraction and subtraction to division:
\[ 3^2 \times 2^2 - (6^2 \div 9) + 1^2 = 33 \]

### Step 8: Recalculate with the new operations
Now we recalculate:
1. Calculate \(6^2 \div 9\):
\[ 36 \div 9 = 4 \]

2. Substitute back into the equation:
\[ 9 \times 4 - 4 + 1 = 33 \]

3. Calculate \(9 \times 4\):
\[ 36 - 4 + 1 = 33 \]

4. Finally, simplify:
\[ 36 - 4 = 32 \quad \text{and} \quad 32 + 1 = 33 \]

### Conclusion
Thus, the equation holds true, and we have verified that the correct operations lead to the result of 33.

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