1. **State the problem:** Evaluate the expression $$2^4 + (11 + 13) - (1 + 5) \div 2 \cdot 3$$. 2. **Recall the order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). 3. **Step 1:** Simplify inside parentheses: $$(11 + 13) = 24$$ $$(1 + 5) = 6$$ So the expression becomes: $$2^4 + 24 - 6 \div 2 \cdot 3$$ 4. **Step 2:** Calculate the exponent: $$2^4 = 16$$ Expression now: $$16 + 24 - 6 \div 2 \cdot 3$$ 5. **Step 3:** Perform division and multiplication from left to right: First division: $$6 \div 2 = \cancel{6} \div \cancel{2} = 3$$ Then multiplication: $$3 \cdot 3 = 9$$ Expression now: $$16 + 24 - 9$$ 6. **Step 4:** Perform addition and subtraction from left to right: $$16 + 24 = 40$$ $$40 - 9 = 31$$ **Final answer:** $$31$$