**Simplify.**
*Rewrite the expression in the form \[5^n\].*

\[(5^{-8})(5^{-10})=\]


To simplify the expression \((5^{-8})(5^{-10})\) and rewrite it in the form \(5^n\), we can use the properties of exponents.

### Step 1: Apply the Product Rule for Exponents
The product rule for exponents states that:

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

Using this rule:

\[
(5^{-8})(5^{-10}) = 5^{-8 + (-10)}
\]

### Step 2: Simplify the Exponent
Simplify the exponent by adding:

\[
5^{-8 + (-10)} = 5^{-18}
\]

### Final Answer
The simplified expression is:

\[
\boxed{5^{-18}}
\]

Would you like any additional explanations or details?

Here are 5 related questions:
1. How would you simplify \(5^3 \times 5^4\)?
2. What is the value of \(5^{-18}\) as a decimal?
3. How do you simplify \(\frac{5^{-8}}{5^{-10}}\)?
4. What is the general rule for multiplying powers with the same base?
5. How do negative exponents affect the value of an expression?

**Tip:** When multiplying two powers with the same base, add the exponents.

Learn how to simplify the expression \( (5^{-8})(5^{-10}) \) involving exponents using the product rule for exponents. Follow a step-by-step explanation with a focus on applying exponent rules effectively. Suitable for Grades 7-9 students studying exponentiation.

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