Let's solve the expression \( (17)^{3.5} \times (17)^7 \) and verify if it equals \( 17^8 \).

### Step 1: Apply the Product Rule for Exponents
The product rule for exponents states that:
\[
a^m \times a^n = a^{m+n}
\]
In this case:
\[
(17)^{3.5} \times (17)^7 = 17^{3.5 + 7}
\]
\[
= 17^{10.5}
\]

### Step 2: Compare with \( 17^8 \)
Now, we compare \( 17^{10.5} \) with \( 17^8 \).

Clearly:
\[
17^{10.5} \neq 17^8
\]

### Conclusion:
The expression \( (17)^{3.5} \times (17)^7 \) is **not** equal to \( 17^8 \). Instead, it simplifies to \( 17^{10.5} \).

Would you like more details or have any questions?

---

1. What is the product rule for exponents?
2. How do you combine exponents with the same base?
3. Why doesn't \( 17^{10.5} \) equal \( 17^8 \)?
4. What are the steps to simplify exponent expressions?
5. How does exponent addition work for fractional exponents?
6. Can you simplify \( a^{m+n} \) when \( m \) or \( n \) is a decimal?
7. How would you calculate \( 17^{10.5} \) using a calculator?
8. What are the common mistakes when multiplying exponent expressions?

**Tip:** When multiplying terms with the same base, always add the exponents, regardless of whether they are integers or fractions.

Explore the solution to the problem \( (17)^{3.5} \times (17)^7 = 17^8 \). Learn how to apply the product rule for exponents and understand why \( 17^{10.5} \neq 17^8 \). Suitable for Grades 7-9.

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