To simplify the expression and rewrite it in the form [tex]\(5^n\)[/tex], follow these steps:
1. Identify the base and exponents: The base in both terms is 5, and the exponents are -8 and -10.
2. Use the properties of exponents: According to the properties of exponents, specifically the multiplication rule for powers of the same base, we have
[tex]\[
a^m \cdot a^n = a^{m+n}
\][/tex]
Here, [tex]\(a = 5\)[/tex], [tex]\(m = -8\)[/tex], and [tex]\(n = -10\)[/tex].
3. Add the exponents: Combine the exponents from the terms by adding them together:
[tex]\[
-8 + (-10) = -8 - 10 = -18
\][/tex]
4. Rewrite the expression: Now that we have the exponent sum, rewrite the expression in the simplified form
[tex]\[
5^{-18}
\][/tex]
Hence, the simplified expression is
[tex]\[
\boxed{5^{-18}}
\][/tex]
