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Let's go through the questions step by step and simplify each expression using the rules of scientific notation.

### General rule for multiplying or dividing in scientific notation:
- **Multiplication**: \( (a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{m+n} \)
- **Division**: \( \frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n} \)

---

### 1. \( (7 \times 10^8) \times (9 \times 10^6) \)

\[
(7 \times 9) \times 10^{8 + 6} = 63 \times 10^{14}
\]
Convert to scientific notation:
\[
6.3 \times 10^{15}
\]
**Answer**: \( 6.3 \times 10^{15} \)

---

### 2. \( \frac{3 \times 10^4}{8 \times 10^1} \)

\[
\frac{3}{8} \times 10^{4 - 1} = 0.375 \times 10^3
\]
Convert to scientific notation:
\[
3.75 \times 10^2
\]
**Answer**: \( 3.75 \times 10^2 \)

---

### 3. \( \frac{4 \times 10^9}{5 \times 10^7} \)

\[
\frac{4}{5} \times 10^{9 - 7} = 0.8 \times 10^2
\]
Convert to scientific notation:
\[
8.0 \times 10^1
\]
**Answer**: \( 8.0 \times 10^1 \)

---

### 4. \( (2 \times 10^3) \times (3 \times 10^4) \)

\[
(2 \times 3) \times 10^{3 + 4} = 6 \times 10^7
\]
**Answer**: \( 6 \times 10^7 \)

---

### 5. \( (3 \times 10^7) \times (9 \times 10^6) \)

\[
(3 \times 9) \times 10^{7 + 6} = 27 \times 10^{13}
\]
Convert to scientific notation:
\[
2.7 \times 10^{14}
\]
**Answer**: \( 2.7 \times 10^{14} \)

---

### 6. \( \frac{4 \times 10^5}{16 \times 10^2} \)

\[
\frac{4}{16} \times 10^{5 - 2} = 0.25 \times 10^3
\]
Convert to scientific notation:
\[
2.5 \times 10^2
\]
**Answer**: \( 2.5 \times 10^2 \)

---

### 7. \( \frac{9 \times 10^5}{10 \times 10^3} \)

\[
\frac{9}{10} \times 10^{5 - 3} = 0.9 \times 10^2
\]
Convert to scientific notation:
\[
9.0 \times 10^1
\]
**Answer**: \( 9.0 \times 10^1 \)

---

### 8. \( (11 \times 10^4) \times (7 \times 10^2) \)

\[
(11 \times 7) \times 10^{4 + 2} = 77 \times 10^6
\]
Convert to scientific notation:
\[
7.7 \times 10^7
\]
**Answer**: \( 7.7 \times 10^7 \)

---

Would you like more details on any of these steps, or do you have any questions? 

### 5 Related Questions:
1. What are the rules for adding numbers in scientific notation?
2. How can you quickly convert a number to scientific notation?
3. What are the main differences between multiplying and dividing in scientific notation?
4. How do you adjust when the base number exceeds 10 during multiplication?
5. What real-world applications use scientific notation frequently?

### Tip:
Always double-check the exponent rules when multiplying or dividing—small mistakes in exponents can lead to incorrect answers!

Simplify each problem and express the answer in scientific notation.

Learn how to simplify problems using scientific notation. This guide covers the multiplication and division of numbers in scientific notation and applying exponent rules, suitable for students in Grades 6-8.

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