Presentation on theme: "8.1 Multiplying Monomials"— Presentation transcript:
1 8.1 Multiplying Monomials What you’ll learn:To multiply monomialsTo simplify expressions involving powers of monomials
2 VocabMonomial – 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, ¼a²bnot monomials: 5+x, , 3x-8Constants – monomials with no variableRecall: 5x³exponentcoefficientbase
3 Product of PowersTo 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
4 Power of a PowerWhen an exponent is raised to another power, multiply the exponents. (a²)³=a⁶ (a²)(a²)(a²)=a⁶ (x)⁴=x⁴
5 Power of a ProductTo 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. -535x-4y9-x5. ⅔x²y³YesNo (addition)No (subtraction)No (division by a variable)yes