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8.1 Multiplying Monomials

Discover how to multiply monomials and simplify expressions involving powers of monomials. Understand terms like monomial and constant, and learn rules for combining like bases, powers of powers, and fractions. Practice with examples provided.

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8.1 Multiplying Monomials

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  1. 8.1 Multiplying Monomials What you’ll learn: To multiply monomials To simplify expressions involving powers of monomials

  2. Vocab • Monomial – a number, a variable, or the product of a number and one or more variables. NO addition, subtraction or division by a variable! examples: 6x, 9, -4xy, ¼a²b not monomials: 5+x, , 3x-8 • Constants – monomials with no variable • Recall: 5x³ exponent coefficient base

  3. Product of Powers To multiply two powers that have the same base, add the exponents. a⁴a⁵=a⁹ (aaaa)(aaaaa)=a⁹ Remember if there are coefficients to MULTIPLY them DON’T ADD THEM!! Ex: (5x³)(-3x²)=-15x⁵

  4. Power of a Power When an exponent is raised to another power, multiply the exponents. (a²)³=a⁶ (a²)(a²)(a²)=a⁶ (x)⁴=x⁴

  5. Power of a Product To find the power of a product, raise each part to that power. (3x²)⁴=(3⁴)(x²)⁴=81x⁸ (a²b³)³=a⁶b⁹ FYI: A negative number raised to an even power will be positive. A negative number raised to an odd power will be negative.

  6. Simplifying Monomial Expressions: • All like-bases are combined. • No powers of powers. • Fractions are simplified.

  7. Determine whether each expression is a monomial. Write yes or no. • -53 • 5x-4y • 9-x 5. ⅔x²y³ • Yes • No (addition) • No (subtraction) • No (division by a variable) • yes

  8. Simplify • (xy²)(x³y) x⁴y³ • (-5x⁴)² 25x⁸ • (2a²b³c⁴)(-5ab²c²) -10a³b⁵c⁶ 4. • [(x²)³]² (x⁶)² • (3x²y)²(2x⁴y³)³ • (-5x³)²(-2x⁵)³

  9. Homeworkp. 41316-44 even

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