To simplify the expression \( 150^9 \times 150^{33} \), you can use the property of exponents that states \( a^m \times a^n = a^{m+n} \).
Applying this property here:
\[ 150^9 \times 150^{33} = 150^{9 + 33} = 150^{42} \]
Thus, the simplified expression is:
\[ \boxed{150^{42}} \]