-5(2)^2 = -5 \times 4 = -20 - United Radiology

["# Solving -5(2)²: Why It’s More Than Just a Basic Algebra Equation", "Understanding algebraic expressions can sometimes feel overwhelming—but today, we break down one common equation that trips up learners: -5(2)² = -5 × 4 = -20. At first glance, this simplifies clearly—but many wonder: why do we square 2 when it’s placed after the multiplication? In this article, we explain the math step-by-step, clarify common misconceptions, and explore how proper handling of exponents and operations leads to accurate results.", "## The Expression: Why Exponents Come After Parentheses", "Let’s examine the expression:", "-5(2)²", "The parentheses indicate that 2 is the base, but notice the exponent is written after the parentheses. This order matters under PEMDAS/BODMAS rules—the standard order of operations:", "1. Parentheses/Brackets
\n2. Exponents/Orders (e.g., squaring)
\n3. Multiplication and Division (left to right)
\n4. Addition and Subtraction (left to right)", "Because the exponent ² applies to 2 alone, not to (-5 × 2), we must first calculate 2² = 4 before multiplying by -5.", "## Breaking Down the Calculation Step by Step", "### Step 1: Evaluate the exponent
\nFirst, calculate (2)²:
\n[
\n2^2 = 4
\n]", "### Step 2: Perform the multiplication
\nNow multiply the result by -5:
\n[
\n-5 \ imes 4 = -20
\n]", "Thus,
\n-5(2)² = -20", "Why isn’t it –5×2 first, then squared? Because squaring a signed number means squaring its absolute value and keeping the sign. Since (2^2 = 4), no negative sign remains after exponentiation.", "## Common Mistake: Forgetting Exponent Priority", "A frequent error occurs when someone computes:
\n[
\n-5 \ imes 2^2 \quad \ ext{interpreted as} \quad (-5 \ imes 2)^2 = (-15)^2 = 225
\n]
\nThis misapplication treats the exponent as acting on the full-Brackets value, not just the 2. Correct grouping is key: exponentiation applies only to the immediately preceding item unless parentheses explicitly alter scope.", "## Why This Matters in Algebra", "Mastering the proper order of operations prevents errors across more complex problems—from quadratic equations to polynomial simplification. Correct exponent handling ensures consistent, accurate results essential for advanced math concepts.", "## Final Summary", "To clarify:
\n- Parentheses define the base for exponentiation: ( (2)^2 = 4 )
\n- Exponents come before multiplication in order of operations
\n- Only the 2 is squared; -5 is multiplied afterward", "So,
\n[
\n-5(2)^2 = -5 \ imes 4 = -20
\n]", "Remember: Parentheses first, exponents next, then multiplication—this rule is your foundation for mastering algebra.", "---", "Keywords: -5(2)² explanation, why squaring comes before multiplication, order of operations algebra, exponent rules, algebra basics, simplify -5×4 correctly, math error fix -5(2)^2, how to calculate -5(2)^2, proper exponent handling", "Meta Description:
\nLearn exactly why -5(2)² equals -20. Discover the correct order of operations: evaluate exponents before multiplication, avoid common algebraic mistakes, and build stronger math fundamentals.", "---", "Next time you see an expression like -5(2)², remember: exponentiation applies first to the enclosed quantity, then multiply—just not before!"]