Let's solve the expression step by step:

Given expression:

\[
(-7) \times \left( (-8) - (-6) + \frac{8}{(-2)^3} \right)
\]

### Step 1: Simplify inside the parentheses
- First, evaluate \((-2)^3\):
  \[
  (-2)^3 = -8
  \]
- Next, evaluate the division:
  \[
  \frac{8}{-8} = -1
  \]

Now the expression inside the parentheses becomes:
\[
(-8) - (-6) + (-1)
\]

### Step 2: Simplify the subtraction and addition:
- \((-8) - (-6) = -8 + 6 = -2\)
- Now we have:
  \[
  -2 + (-1) = -2 - 1 = -3
  \]

### Step 3: Multiply by \(-7\):
\[
-7 \times (-3) = 21
\]

Thus, the value of the expression is \(21\).

Would you like further clarification on any of the steps?

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Here are 5 related questions for you to try:
1. Simplify \((-5) \times ((-9) - (-4) + \frac{6}{(-3)^2})\).
2. Evaluate \((-6) \times ((-7) - 8 + \frac{12}{(-2)^2})\).
3. What is the result of \((-4) \times ((-3) - (-5) + \frac{9}{(-3)^2})\)?
4. Solve \((-9) \times ((-8) + 4 - \frac{10}{(-5)})\).
5. Calculate \((-10) \times ((-12) + (-5) + \frac{15}{(-3)^2})\).

**Tip**: Always apply the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) when simplifying expressions.

This solution guides you through simplifying the algebraic expression (-7)×((-8)-(-6)+8÷(-2)^3) step by step. It involves using the order of operations (PEMDAS), exponentiation, and multiplication. Suitable for students in Grades 7-9.

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