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

xy d. c. b. a. ReasonMonomial?Expression Example 1-1a Determine whether each expression is a monomial. Explain your reasoning. The expression is the product of two variables. yes The expression is the product of a number and two variables. yes The expression involves subtraction, not the product, of two variables. no is a real number and an example of a constant.

d. c. b. a. ReasonMonomial?Expression Example 1-1b Determine whether each expression is a monomial. Explain your reasoning. yes no The expression involves subtraction, not the product, of two variables. no Single variables are monomials.yes The expression is the quotient, not the product, of two variables. The expression is the product of a number,, and two variables.

Exponent Review

Products of Powers To multiply two powers that have the same base, add the exponents. Examples: a m · a n = a n+m

Power of Powers To find the power of a power, multiply the exponents. Examples: (a m ) n = a n+m

Power of a Product To find the power of a product, find the power of each factor and multiply. Examples: (ab) n = a n b n

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 Simplifying a Monomial

Example 1-2a Simplify. Commutative and Associative Properties Product of Powers Simplify. Answer:

Example 1-2b Simplify. Communicative and Associative Properties Product of Powers Simplify. Answer:

Example 1-2c Simplify each expression. a. b. Answer:

Example 1-3a Simplify Simplify. Answer: Power of a Power Simplify. Power of a Power

Example 1-3b Simplify Answer:

Example 1-4a Geometry Find the volume of a cube with a side length Simplify. Answer: VolumeFormula for volume of a cube Power of a Product

Example 1-4b Express the surface area of the cube as a monomial. Answer:

Example 1-5a Simplify Power of a Power Power of a Product Power of a Power

Example 1-5b Commutative Property Answer: Power of Powers

Example 1-5c Simplify Answer:

Investigation

Homework 8-1 Multiplying Monomials Two Pages Even Problems