Solve `17+22 div 11 times (18 div 13)^2-13`

Answer

To solve the expression \( 17 + 22 \div 11 \times (18 \div 13)^2 - 13 \), we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step-by-Step Solution:

1. **Evaluate the expression inside the parentheses**:
\[ 18 \div 13 \]
This gives us approximately \( 1.3846 \).

**Hint**: Always start by solving expressions inside parentheses first.

2. **Square the result from step 1**:
\[ (18 \div 13)^2 \approx (1.3846)^2 \approx 1.9201 \]

**Hint**: Remember to square the result after dividing.

3. **Now substitute back into the original expression**:
\[ 17 + 22 \div 11 \times 1.9201 - 13 \]

**Hint**: Replace the parentheses with the squared result.

4. **Perform the division**:
\[ 22 \div 11 = 2 \]

**Hint**: Division comes before multiplication in the order of operations.

5. **Now multiply the result from step 4 with the squared result from step 2**:
\[ 2 \times 1.9201 \approx 3.8402 \]

**Hint**: After division, perform multiplication next.

6. **Substitute back into the expression**:
\[ 17 + 3.8402 - 13 \]

**Hint**: Keep track of the order of operations as you substitute back.

7. **Now perform the addition**:
\[ 17 + 3.8402 \approx 20.8402 \]

**Hint**: Addition is straightforward; just combine the numbers.

8. **Finally, perform the subtraction**:
\[ 20.8402 - 13 \approx 7.8402 \]

**Hint**: Subtract the last number to get the final result.

### Final Answer:
\[ \approx 7.8402 \]