https://file.aiquickdraw.com/mathbot/file/1726827392937vm0bnrem.jpg

Let's fully simplify the given expression:

\[
5n^3p^8 \times 9n^6p^2 \div 3n^2p^4
\]

### Step-by-Step Simplification:

1. **Multiply the terms** \(5n^3p^8\) and \(9n^6p^2\):
   \[
   5 \times 9 = 45
   \]
   \[
   n^3 \times n^6 = n^{3+6} = n^9
   \]
   \[
   p^8 \times p^2 = p^{8+2} = p^{10}
   \]
   So, the multiplication yields:
   \[
   45n^9p^{10}
   \]

2. **Now, divide the result by \(3n^2p^4\)**:
   \[
   \frac{45}{3} = 15
   \]
   \[
   \frac{n^9}{n^2} = n^{9-2} = n^7
   \]
   \[
   \frac{p^{10}}{p^4} = p^{10-4} = p^6
   \]

Thus, the fully simplified expression is:
\[
15n^7p^6
\]

If you'd like any clarifications, feel free to ask!

Here are 5 related questions you might explore:
1. How do we simplify expressions with variables raised to powers?
2. What are the rules of exponents for multiplying and dividing terms?
3. How would the result change if we had additional variables?
4. Can you apply these exponent rules to expressions involving negative powers?
5. What happens if terms in the denominator have larger exponents than in the numerator?

**Tip:** Always remember that when dividing powers with the same base, subtract the exponents!

Fully simplify the following expression: 5n^3p^8 * 9n^6p^2 ÷ 3n^2p^4

Simplify the expression 5n^3p^8 * 9n^6p^2 ÷ 3n^2p^4 using the rules of exponents for multiplication and division. This step-by-step guide walks you through multiplying and dividing powers with the same base, suitable for students in Grades 9-10.

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