8.1 Multiplying Monomials

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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. 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

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

Homework p. 413 16-44 even