Let's break down the given expression:

\[
(8.8 \times 2.25)(10^2 \times 10^{-2})
\]

### Step 1: Multiply the numbers inside the first parentheses.

\[
8.8 \times 2.25 = 19.8
\]

### Step 2: Multiply the powers of 10.

Using the rule of exponents: \( a^m \times a^n = a^{m+n} \), we get:

\[
10^2 \times 10^{-2} = 10^{2-2} = 10^0 = 1
\]

### Step 3: Multiply the results from Step 1 and Step 2.

\[
19.8 \times 1 = 19.8
\]

So, the final result is:

\[
\boxed{19.8}
\]

Would you like further details, or have any questions?

Here are 5 related questions to extend your understanding:
1. What is the rule for multiplying numbers with powers of 10?
2. How would the result change if the powers of 10 were different, say \(10^3\) and \(10^{-1}\)?
3. Can you break down the multiplication of decimals like \(8.8 \times 2.25\) using long multiplication?
4. What happens if the powers of 10 had addition or subtraction instead of multiplication?
5. How does \(10^0 = 1\) affect larger calculations?

**Tip:** When multiplying powers of 10, just add or subtract their exponents for a quick result!

Learn how to solve the multiplication problem (8.8 x 2.25)(10^2 x 10^-2) step-by-step. This guide explains how to multiply decimals and apply exponent rules, showing how to handle powers of 10 effectively. Suitable for students in Grades 6-8.

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