a. – b. 8 – 19 c. – 15 – (– 15) d. – 10 + (– 46) Problems of the Day Simplify. e. f. g. h.

Algebra 1 ~ Chapter 8.1 Multiplying Monomials

Monomials A monomial is a number, a variable, or a product of a number and one or more variables. (ex. 4x, 3ab, y 3, ) An expression involving the division of variables is not a monomial. (ex. ) Monomials that are real numbers are called constants. (ex. 4, − 100)

Exponents An expression in the form x n is called a power and represents the product you obtain when x is used as a factor n times. The number x is the base, and the number n is the exponent. For example, 2 5 = or 32

Look for the pattern when multiplying powers… = or = or = or 6 5 x 5 x 4 = xxxxx xxxx or x 9 a m a n = a m+n To multiply two powers that have the same base, add the exponents.

Example 1 – Simplify each expression a.) x 3 x 5 b.) a a 6 c.) 2y 3 4y 8 y 2 d.) − 3m 2 5m 4 e.) a 2 b 2 a 3 b 5 = x 8 = a 7 = 8y 13 = − 15m 6 = a 5 b 7

Look for the pattern when finding the power of a power… (2 4 ) 3 = or 2 12 (3 2 ) 5 = or 3 10 (x 3 ) 2 = x 3 x 3 or x 6 (a m ) n = a m n (Power of a power) To find the power of a power, multiply the exponents.

Look for the pattern when finding a power of a product… (2x 5 ) 2 = (2x 5 ) (2x 5 ) or 4x 10 (2x 5 ) 2 = (2) 2 (x 5 ) 2 or 4x 10 ( − 3a 3 b) 2 = ( − 3) 2 (a 3 ) 2 (b) 2 or 9a 6 b 2 (ab) m = a m b m (Power of products) To find the power or a product, find the power of each factor and multiply

Example 2 – Simplify each expression a.) (x 3 ) 6 b.) (ab) 3 c.) (2y 3 ) 4 d.) ( − 3m 2 n) 3 e.) [(a 2 ) 3 ] 4 = x 18 = a 3 b 3 = 16y 12 = − 27m 6 n 3 = [a 6 ] 4 = a 24

Algebra 1 ~ Chapter 8.2 Dividing Monomials

= y 6 − 2 = y 4

Example 1: Simplify each expression. A. B.C.

D. Example 1: Simplify each expression. E. = 6x 7-2 ∙ y 3-1 ∙ z 5-1 = 6x 5 y 2 z 4

Another example…

Example 2 – Simplify each expression Use the Power of a Quotient Property. A.)

Example 2B - Simplify

Anything divided by itself is equal to 1! x = x -3 =

Example 3: Simplify each expression. A.) 4 –3 B.) 7 0 7º = 1 C.) (–5) –4 D.) –5 –4

An expression that contains negative or zero exponents is not considered to be simplified. Expressions should be rewritten with only positive exponents. What if you have an expression with a negative exponent in a denominator, such as ? or Definition of a negative exponent

Example 4: Simplify each expression A.) 7w –4 B.)

C.) and

Lesson Wrap-Up Simplify each expression. a. c. d. b. = y 7 = 64d 6 = – 32a 17 b 17 = – 720u 22 v 29

Lesson Wrap Up – Simplify each expression below. 1.)2.)3.)

Assignment Homework 8.1/8.2 Study Guide