`55xx55div11xx9div9div(495)/(11)=?`

Options

A. `(45)/(8)`
B. `(65)/(11)`
C. `(52)/(9)`
D. `(55)/(9)`

Explanation

To solve the expression \( 55 \times 55 \div 11 \times 9 \div 9 \div \frac{495}{11} \), we will simplify it step by step.

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{55 \times 55 \times 11 \times 9 \times 9}{9 \times 11 \times 495} \]

### Step 2: Cancel out common factors
We can cancel out the \( 11 \) in the numerator with one \( 11 \) in the denominator:
\[ \frac{55 \times 55 \times 9 \times 9}{9 \times 495} \]

### Step 3: Cancel the \( 9 \)
Now, we can cancel one \( 9 \) from the numerator with one \( 9 \) in the denominator:
\[ \frac{55 \times 55 \times 9}{495} \]

### Step 4: Simplify \( 495 \)
Next, we can simplify \( 495 \) as follows:
\[ 495 = 55 \times 9 \]
So we can replace \( 495 \) in the denominator:
\[ \frac{55 \times 55 \times 9}{55 \times 9} \]

### Step 5: Cancel \( 55 \) and \( 9 \)
Now we can cancel \( 55 \) and \( 9 \) in the numerator and denominator:
\[ \frac{55}{1} = 55 \]

### Step 6: Final result
Thus, the final answer is:
\[ \frac{55}{9} \]

### Summary of Steps:
1. Rewrite the expression.
2. Cancel common factors.
3. Simplify \( 495 \).
4. Cancel remaining factors.
5. Obtain the final result.