Using the Product Rule of Exponents, which states that \(a^m \times a^n = a^{m+n}\), we can combine the two powers of 1:
\[ 1^9 \times 1^8 = 1^{9+8} = 1^{17}. \]
Since any power of 1 is still 1, we can conclude that:
\[ 1^9 \times 1^8 = 1. \]
So, the equivalent form of \(1^9 \times 1^8\) is \(\boxed{1}\).