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8.1 Multiplying Monomials. What you’ll learn: To multiply monomials To simplify expressions involving powers of monomials. 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!
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8.1 Multiplying Monomials What you’ll learn: To multiply monomials To simplify expressions involving powers of monomials
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
Product of Powers To multiply two powers that have the same base, add the exponents. a⁴a⁵=a⁹ (aaaa)(aaaaa)=a⁹ Remember if there are coefficients to MULTIPLY them DON’T ADD THEM!! Ex: (5x³)(-3x²)=-15x⁵
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
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.
Simplifying Monomial Expressions: • All like-bases are combined. • No powers of powers. • Fractions are simplified.
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
Simplify • (xy²)(x³y) x⁴y³ • (-5x⁴)² 25x⁸ • (2a²b³c⁴)(-5ab²c²) -10a³b⁵c⁶ 4. • [(x²)³]² (x⁶)² • (3x²y)²(2x⁴y³)³ • (-5x³)²(-2x⁵)³