1. **State the problem:** Evaluate the expression $$34 - 2 \cdot 8 + 12 \div 4$$ and find the prime factorization of 64. 2. **Evaluate the expression:** - Use the order of operations (PEMDAS/BODMAS): multiplication and division before addition and subtraction. - Calculate multiplication: $$2 \cdot 8 = 16$$ - Calculate division: $$12 \div 4 = 3$$ - Substitute back: $$34 - 16 + 3$$ - Perform subtraction and addition from left to right: $$34 - 16 = 18$$ $$18 + 3 = 21$$ 3. **Prime factorization of 64:** - 64 is a power of 2. - Divide repeatedly by 2: $$64 \div 2 = 32$$ $$32 \div 2 = 16$$ $$16 \div 2 = 8$$ $$8 \div 2 = 4$$ $$4 \div 2 = 2$$ $$2 \div 2 = 1$$ - So, $$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{6}$$ **Final answers:** - Expression value: $$21$$ - Prime factorization of 64: $$2^{6}$$