To simplify the expression \(1^9 \times 1^8\), we can use the property of exponents that states \(a^m \times a^n = a^{m+n}\).
In your case, both terms have a base of 1:
\[ 1^9 \times 1^8 = 1^{9+8} = 1^{17} \]
So, the base is \(1\) and the exponent is \(17\).