Multiply the expressions: 8x⁶y⁹ × 9x²y⁴ = 72x⁸y¹³
["Multiply the Expressions: A Step-by-Step Guide to 8x⁶y⁹ × 9x²y⁴ = 72x⁸y¹³", "Multiplication of algebraic expressions is a foundational skill in algebra that helps simplify equations, scale terms, and solve equations efficiently. In this article, we will explore how to multiply the expressions 8x⁶y⁹ and 9x²y⁴, demonstrating why their product equals 72x⁸y¹³. Whether you’re a student mastering exponents or a lifelong learner brushing up on algebra basics, this guide provides clear, detailed steps to understand the process.", "---", "### Understanding the Multiplication of Monomials", "When multiplying monomials (expressions with a single term), we follow a simple rule: multiply the coefficients and add the exponents of like bases.", "The general multiplication rule is:\n(a × bⁿ)(c × dᵐ) = ac × bⁿ⁺ᵐ × dᵐ\nThat is, coefficients multiply, while exponents of variables with the same base are added.", "---", "### Step 1: Identify the coefficients and variables", "We are multiplying:\n8x⁶y⁹ × 9x²y⁴", "Break it down:", "- Coefficients: 8 and 9\n- Variable x: exponent 6 and 2\n- Variable y: exponent 9 and 4", "---", "### Step 2: Multiply the coefficients", "Multiply the numbers:\n8 × 9 = 72", "---", "### Step 3: Add the exponents of like variables", "For variable x:\n6 (from 8x⁶) + 2 (from 9x²) = 8", "For variable y:\n9 (from 8x⁶y⁹) + 4 (from 9x²y⁴) = 13", "---", "### Step 4: Combine results", "Putting everything together:\n72 × x⁸ × y¹³ = 72x⁸y¹³", "---", "### Final Result:\n$$\n\boxed{8x^6y^9 \ imes 9x^2y^4 = 72x^8y^{13}}\n$$", "---", "### Why This Matters", "Understanding this process strengthens your ability to simplify complex expressions, solve equations, and manipulate polynomial terms—key skills in algebra, calculus, and advanced mathematics.", "Remember:\n- Coefficients multiply arithmetically\n- Like bases have exponents added, not multiplied\n- Notation must reflect final exponents clearly", "---", "Keywords for SEO:\nmultiply algebraic expressions, how to multiply 8x⁶y⁹ and 9x²y⁴, algebra multiplication steps, coefficient and variable exponent rules, simplify 72x⁸y¹³, exponents in multiplication, polynomial multiplication guide", "---", "Start mastering expression multiplication today—exponent rules simplify your math forever!"]
