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To solve this problem, let’s break down the expression given:

\[
\frac{(5 \times 10^{-3}) + (6 \times 10^{-3})}{2.2 \times 10^4}
\]

### Step 1: Simplify the Numerator

The numerator is:
\[
(5 \times 10^{-3}) + (6 \times 10^{-3})
\]

Since both terms have the same power of 10, we can factor out \(10^{-3}\):
\[
= (5 + 6) \times 10^{-3} = 11 \times 10^{-3}
\]

So the numerator simplifies to \(11 \times 10^{-3}\).

### Step 2: Divide by the Denominator

Now we have:
\[
\frac{11 \times 10^{-3}}{2.2 \times 10^4}
\]

This can be simplified by dividing the coefficients (11 and 2.2) and handling the powers of 10 separately:
\[
\frac{11}{2.2} \times \frac{10^{-3}}{10^4}
\]

1. **Divide the coefficients**: \(\frac{11}{2.2} = 5\).
2. **Divide the powers of 10**: \(10^{-3} \div 10^4 = 10^{-3 - 4} = 10^{-7}\).

So the entire expression simplifies to:
\[
5 \times 10^{-7}
\]

### Answer

The equivalent expression is:
\[
\boxed{5 \times 10^{-7}}
\]

Would you like a deeper explanation or have any further questions?

---

Here are some related questions to expand your understanding:
1. How would this approach change if the exponents were different in the terms to be added?
2. What would happen if the denominator had a negative exponent?
3. How does scientific notation help simplify multiplication and division?
4. Can you explain why we can factor out the same powers of 10 in addition?
5. What are some real-world applications where scientific notation is especially useful?

**Tip:** Always check if terms have the same power of 10 when adding in scientific notation—it can simplify calculations significantly!

Which expression is equivalent to the following? 
\(\frac{(5 \times 10^{-3}) + (6 \times 10^{-3})}{2.2 \times 10^4}\)

Learn how to find the equivalent expression of \(\frac{(5 \times 10^{-3}) + (6 \times 10^{-3})}{2.2 \times 10^4}\) using scientific notation and exponent rules. This problem is suitable for students in Grades 8-10 and covers key concepts such as scientific notation and simplifying expressions.

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