Let's break down the expression step by step:

Given expression:
\[ 4(1 + 8 \cdot 6) - 6^2 \]

1. **Evaluate inside the parentheses**:
   \[
   8 \cdot 6 = 48
   \]
   So, the expression inside the parentheses becomes:
   \[
   1 + 48 = 49
   \]

2. **Multiply by 4**:
   \[
   4 \cdot 49 = 196
   \]

3. **Evaluate the exponent**:
   \[
   6^2 = 36
   \]

4. **Subtract**:
   \[
   196 - 36 = 160
   \]

So, the final result is **160**.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would the expression change if the exponent were \(6^3\) instead?
2. What happens if the multiplication sign in the parentheses is replaced by addition?
3. How do you evaluate \(4(2 + 7 \cdot 5) - 3^2\)?
4. How would the expression evaluate if there were a division by 2 after the subtraction?
5. What is the result if you change the 4 to an 8 in the expression?

**Tip**: Always remember the order of operations, often remembered by PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Master the order of operations with a detailed step-by-step solution to the expression 4(1 + 8 · 6) − 6^2. This problem involves evaluating expressions with parentheses, exponents, multiplication, and subtraction, making it ideal for students in Grades 6-8.

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