To solve the expression \((13+7 \cdot 5) \div [-6 + (9+1 \cdot 3)] + 8\), follow the order of operations (PEMDAS/BODMAS):

1. **Parentheses/Brackets**: Simplify inside parentheses first.
2. **Exponents/Orders**: Not applicable here.
3. **Multiplication and Division**: From left to right.
4. **Addition and Subtraction**: From left to right.

### Step-by-step Solution:

1. **Inside Parentheses/Brackets**:
   - Simplify \((9 + 1 \cdot 3)\):
     \[
     9 + 1 \cdot 3 = 9 + 3 = 12
     \]

   - Now substitute back:
     \[
     (13 + 7 \cdot 5) \div [-6 + 12] + 8
     \]

2. **Further Simplify**:
   - Simplify \(13 + 7 \cdot 5\):
     \[
     7 \cdot 5 = 35
     \]
     \[
     13 + 35 = 48
     \]

   - Simplify \(-6 + 12\):
     \[
     -6 + 12 = 6
     \]

   - Now substitute back:
     \[
     48 \div 6 + 8
     \]

3. **Division**:
   \[
   48 \div 6 = 8
   \]

4. **Addition**:
   \[
   8 + 8 = 16
   \]

So, the final result of the expression \((13+7 \cdot 5) \div [-6 + (9 + 1 \cdot 3)] + 8\) is:

\[
\boxed{16}
\]

Would you like details or have any questions about this solution?

### Relative Questions:
1. What is the result of \( (25 + 3 \cdot 4) \div (2 \cdot 3) + 7 \)?
2. How do you solve \( (18 - 5 \cdot 2) \div [4 + (3 - 1)] + 9 \)?
3. What is the outcome of \( (14 + 6 \cdot 3) \div [8 + (2 \cdot 4)] + 5 \)?
4. Can you simplify \( (22 + 4 \cdot 2) \div [-3 + (7 + 1)] + 6 \)?
5. How to solve \( (15 + 2 \cdot 6) \div [5 + (4 - 2)] + 10 \)?
6. What is the result of \( (9 + 8 \cdot 2) \div [3 + (6 - 1)] + 12 \)?
7. Can you solve \( (17 + 5 \cdot 3) \div [-4 + (8 + 2)] + 14 \)?
8. How do you find the result of \( (12 + 7 \cdot 4) \div [2 + (9 - 3)] + 11 \)?

### Tip:
Always remember to handle operations inside parentheses first and follow the order of operations carefully to avoid mistakes in complex expressions.

Learn how to solve the expression (13+7*5)/[-6+(9+1*3)]+8 with a detailed step-by-step solution. This problem covers order of operations, arithmetic operations, and handling parentheses/brackets. Suitable for students in Grades 5-7.

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