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.