1. **State the problem:** Simplify the expression $$1 - 9 \times 2^2$$. 2. **Recall the order of operations:** According to PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), we first evaluate exponents, then multiplication, and finally subtraction. 3. **Evaluate the exponent:** $$2^2 = 4$$. 4. **Multiply:** $$9 \times 4 = 36$$. 5. **Subtract:** $$1 - 36 = -35$$. **Final answer:** $$-35$$.