(13+7*5)÷[-6+(9+1*3)]+8(13+7*5)÷[-6+(9+1*3)]+8

To solve the given mathematical expression, we need to evaluate it step by step according to the order of operations, often remembered by the acronym PEMDAS:

- **P**arentheses
- **E**xponents
- **M**ultiplication and **D**ivision (from left to right)
- **A**ddition and **S**ubtraction (from left to right)

The expression given is:

\[
(13+7\times5) \div \left[-6+(9+1\times3)\right] + 8
\]

Let's solve it step by step:

### Step 1: Solve Inside Parentheses

1. **First Parentheses**: 
   \[
   13 + 7 \times 5
   \]

   - \(7 \times 5 = 35\)
   - \(13 + 35 = 48\)

   So, the result inside the first parentheses is 48.

2. **Second Parentheses**:
   \[
   -6 + (9 + 1 \times 3)
   \]

   - \(1 \times 3 = 3\)
   - \(9 + 3 = 12\)
   - \(-6 + 12 = 6\)

   So, the result inside the second parentheses is 6.

### Step 2: Substitute Back

The expression now becomes:

\[
48 \div 6 + 8
\]

### Step 3: Division

- \(48 \div 6 = 8\)

### Step 4: Addition

- \(8 + 8 = 16\)

Therefore, the final result of the expression is:

\[
\boxed{16}
\]

### Final Expression Evaluation:

So the expression evaluates to:

\[
16
\]

Would you like further details or have any questions?

### Related Questions

1. What is the importance of following the order of operations in mathematical expressions?
2. How can parentheses affect the outcome of an expression in algebra?
3. What happens if you ignore the order of operations in solving mathematical problems?
4. Can you explain how the distributive property works in expressions with parentheses?
5. How would this expression change if an exponent were added to one of the numbers?
6. Why is division prioritized alongside multiplication in the order of operations?
7. How do nested parentheses work in more complex expressions?
8. How can understanding PEMDAS help in solving algebraic equations efficiently?

### Tip

When solving expressions with multiple operations, always break down each step carefully and follow the order of operations to avoid errors.

Learn how to solve a complex mathematical expression step-by-step using the order of operations (PEMDAS). This problem involves evaluating an expression with parentheses and division, suitable for students in Grades 7-9.

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