The equation given is:

\[
(17)^{3.5} \times (17)^7 = 17^8
\]

To simplify the left side, use the property

To simplify the left side of the equation:

\[
(17)^{3.5} \times (17)^7 = 17^8
\]

We use the property of exponents that states:

\[
a^m \times a^n = a^{m+n}
\]

Here, both bases are the same (17), so we can add the exponents:

\[
(17)^{3.5} \times (17)^7 = 17^{3.5 + 7} = 17^{10.5}
\]

Now, compare this to the right side of the equation, which is \( 17^8 \):

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

Thus, the equation:

\[
(17)^{3.5} \times (17)^7 = 17^8
\]

is **incorrect**.

Would you like any further clarification on exponent rules or have any other questions?

### Related Questions:
1. How do you solve equations involving exponents?
2. What is the rule for multiplying exponents with the same base?
3. How can you simplify expressions with fractional exponents?
4. How do you solve exponential equations?
5. What are the properties of exponents for negative numbers?
6. How do you deal with exponents in algebraic expressions?
7. How can exponent rules be applied to logarithms?
8. What are the real-world applications of exponent rules?

### Tip:
When dealing with exponents, always ensure the bases are the same before applying exponent rules. This helps in simplifying expressions accurately.

Learn how to simplify exponential equations using exponent rules. This problem involves understanding the property of exponents and applying them correctly. Suitable for students in Grades 9-12.

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