Let's break down the expression step by step:

$(-10)^2 - 5(10^3) \times (-2)$

Step 1: Simplify each part of the expression

1. First term: $(-10)^2$

$(-10)^2 = 100$

2. Second term: $-5(10^3) \times (-2)$

• First calculate $10^3 = 1000$.
• Then, multiply by $-5$: $-5 \times 1000 = -5000$.
• Now, multiply by $-2$: $-5000 \times (-2) = 10000$.

Step 2: Combine the results

$100 - 10000 = -9900$

Final Answer:

$\boxed{-9900}$

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Would you like more details or have any other questions about this?

Here are 5 related questions for you:

1. How do we handle negative numbers when squaring them?
2. Why do we calculate powers of 10 as we do in this problem?
3. What is the distributive property and how might it help simplify expressions like this?
4. How can we apply the order of operations (PEMDAS) to similar problems?
5. What would happen if we had parentheses altering the operations in this problem?

Tip: Remember, the order of operations is crucial—always follow the parentheses, exponents, multiplication/division, and then addition/subtraction to avoid mistakes!