Algebra 1A Section 6.1: Multiplying Monomials

Warm-Up  2 2 = ______ ∙ ______ = ______  2 3 = ______ ∙ ______∙ ______ = ______  2 4 = ______ ∙ ______ ∙ ______∙ ______ = ______  3 2 = ______ ∙ ______ = ______  5 3 = ______ ∙ ______ ∙ ­­­______ = ______

Important Concept  Power:__________________________________________  8 2 = ___________NOT the same as _____________  X 5 = _______________NOT the same as __________ An exponent tells how many times we multiply the base by itself 8 x 88 x 2 x. x. x. x. x5x

Example 1 (3 3 )(3 2 ) = 3 5 Example 2 (3x 4 y)(-4x 2 y) 3(-4)x 6 y 2 -12x 6 y 2

PRODUCT OF POWERS the base stays the __________________ ____________ the exponents of the ___________________ base  ____________________ the coefficients (number in front of the base) same Add same Multiply

Your Turn 1 (5y 4 )(3y) 15y 5 Your Turn 2 (-4ab 6 )(-7a 2 b 3 ) 28a 3 b 9

6 th hour Please do on another piece of paper: 

Example 1 Example 3 Example 2 (3xy 4 ) 2 32x2y832x2y8 9x 2 y 8 (-2xy 4 ) 3 (5ab 4 ) 3 (3b 2 ) 2 (-2) 3 x 3 y 12 -8x 3 y 12 (5) 3 a 3 b 12 (3) 2 b 4 (125a 3 b 12 )(9b 4 ) 1125a 3 b 16

Power of Powers _______________________ the exponents of the same ___________________ raise the coefficient to the given __________________________ Multiply base power outside the parenthesis

Your Turn 1 Your Turn 3 Your Turn 2 (2x 2 y) 3 (-3xy 4 ) 4 (2xy) 3 (3x 2 ) 5 8x 6 y 3 81x 4 y x 13 y 3

Are you a master? a)(x 3 ) 4 b) (4 2 )(4 3 )c) x 3 (x 2 ) d) (2xy 2 ) 3 e) f) (-4m 2 n 3 ) 4 g) (-3a 2 b 3 ) 3 h) (n 2 )(n 3 )(n)i) (3xy) 2 (-2x 2 ) 3

Algebra 1A Section 6.2: Dividing Monomials

Warm-Up a)(4 2 )(4 3 ) b) (4xy 2 ) 3 c) (n 4 ) __ = n 12 d) (______) 2 = 81a 2 b 4 c = 1, x 3 y 6 = 48x 3 y 6 3 9ab 2 c 5

Example 1 Example 2Example 3 4x 5 2x 3 4x 3 8x x 2 1 2x or 117,649 4xxxxx 2xxx 4xxx 8xxxxxxxx

DIVIDING MONOMIALS ______________ the coefficients by ____________ or finding the ___________ ___________ the exponents of the ______________ base Divide Reducing the fraction decimal Subtract same

Your Turn 2 Your Turn 1 Your Turn 3 10a 3 5a 3b 6 12b a 2 1 4b 3 1 4

Example 4Your Turn 4 144a 2 b 5 c 12a 3 bc 3 -45x 4 y 2 z 2 15x 3 y 4 z 3 12b 4 ac 2 -3x y 2 z When in doubt….right it out!

ARE YOU A MASTER???? a)(a 3 b 3 )(a 4 b 5 )b) (-7g 3 h 3 ) 3 c) d) e) f) g) h) i)

Warm-up: 1.2.

CAN YOU FIND THE PATTERN?

ZERO EXPONENT PROPERTY a) b)

NEGATIVE EXPONENT PROPERTY EX 1) Your Turn

NEGATIVE EXPONENT PROPERTY EX 2) Your Turn

NEGATIVE EXPONENT PROPERTY EX 3) Your Turn

ARE YOU A MASTER a) b)