Multiplying Monomials Monomials A monomial is a number
Multiplying Monomials
Monomials • A monomial is a number, a variable, or a product of a number and one or more variables. An expression involving the division of variables is NOT a monomial. • Constants are monomials that are real numbers
Determine whether each expression is a monomial. Explain your reasoning. Expression Monomial? a. no b. yes c. yes d. xy yes Reason The expression involves subtraction, not the product, of two variables. The expression is the product of a number and two variables. is a real number and an example of a constant. The expression is the product of two variables.
Determine whether each expression is a monomial. Explain your reasoning. Expression Monomial? Reason yes Single variables are monomials. b. no The expression involves subtraction, not the product, of two variables. c. no The expression is the quotient, not the product, of two variables. a. d. The expression is the product of a yes number, , and two variables.
Exponent Review
Products of Powers • To multiply two powers that have the same base, add the exponents. • Examples: am · an = an+m
Power of Powers • To find the power of a power, multiply the exponents. • Examples: (am)n = an+m
Power of a Product • To find the power of a product, find the power of each factor and multiply. • Examples: (ab)n = anbn
Simplifying a Monomial • To simplify an expression involving monomials, write an equivalent expression in which: – Each base appears exactly once – There are no powers of powers – All fractions are in simplest form
Simplify . Commutative and Associative Properties Product of Powers Answer: Simplify.
Simplify . Communicative and Associative Properties Product of Powers Answer: Simplify.
Simplify each expression. a. Answer: b. Answer:
Simplify Power of a Power Simplify. Power of a Power Answer: Simplify.
Simplify Answer:
Geometry Find the volume of a cube with a side length Volume Formula for volume of a cube Power of a Product Answer: Simplify.
Express the surface area of the cube as a monomial. Answer:
Simplify Power of a Product Power of a Power
Commutative Property Answer: Power of Powers
Simplify Answer:
Investigation
Investigation
Investigation
Homework • 8 -1 Multiplying Monomials Two Pages Even Problems
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