Evaluate the expression: \( 4^3 - 2^4 + 10 \div 2 \).
["# Evaluate the Expression: ( 4^3 - 2^4 + \frac{10}{2} ) – A Clear Step-by-Step Guide", "Evaluating mathematical expressions accurately is a core skill in math, essential for students, teachers, and lifelong learners. Today, we focus on the expression ( 4^3 - 2^4 + \frac{10}{2} ) and provide a complete breakdown of how to evaluate it using proper order of operations. Whether you're learning basic exponent rules, division, and evaluation, or brushing up on PEMDAS/BODMAS, this article will guide you through it step by step.", "---", "### Understanding the Expression", "We start with:", "[\n4^3 - 2^4 + \frac{10}{2}\n]", "This mathematical expression involves three operations:\n- Exponentiation: (4^3) and (2^4)\n- Division: ( \frac{10}{2} )\n- Subtraction and Addition (left to right)", "---", "### Step 1: Apply Order of Operations (PEMDAS/BODMAS)", "The acronym PEMDAS (Parentheses, Exponents, Multiplication & Division, Addition & Subtraction) reminds us the correct sequence to evaluate expressions:", "1. Compute exponents\n2. Perform multiplication and division (from left to right)\n3. Then perform addition and subtraction (from left to right)", "---", "### Step 2: Evaluate Exponents", "First, calculate the exponents:", "- ( 4^3 = 4 \ imes 4 \ imes 4 = 64 )\n- ( 2^4 = 2 \ imes 2 \ imes 2 \ imes 2 = 16 )", "Now substitute back:", "[\n64 - 16 + \frac{10}{2}\n]", "---", "### Step 3: Perform Division", "Next, evaluate the division:", "[\n\frac{10}{2} = 5\n]", "Substitute:", "[\n64 - 16 + 5\n]", "---", "### Step 4: Execute Subtraction and Addition (Left to Right)", "Now work from left to right:", "- ( 64 - 16 = 48 )\n- ( 48 + 5 = 53 )", "---", "### Final Answer", "[\n\boxed{53}\n]", "---", "### Why This Evaluation Matters", "Understanding how to evaluate expressions like (4^3 - 2^4 + \frac{10}{2}) helps build strong foundational math skills. Mastery of exponent rules, division, and the order of operations is crucial for solving more complex algebra, calculus, and applied problems in science and engineering.", "---", "### Practice Tips", "- Revisit exponent rules: powers rule over multiplication and addition.\n- Always simplify division and fractions early.\n- Never skip orders of operations—right-to-left for same-level operations.\n- Check your work by plugging into a calculator or reverse-solving.", "---", "Mastering expression evaluation not only gives the correct answer but also strengthens problem-solving agility. Start small, practice often, and watch your confidence grow in math!", "---", "Keywords: evaluate expression, (4^3 - 2^4 + \frac{10}{2}), mathematical steps, order of operations, PEMDAS, exponent rules, division in math, simplify expression, step-by-step evaluation, math skills learning."]
