1-3 Exponential Notation PGS Associative Property pgs N3: compute powers 9N1: identify properties

Vocabulary 5353 Power or Exponential form Exponent Base

Examples 1) 7 5 means 7∙7∙7∙7∙7 7∙7∙7∙7∙7 2)2x 3 means 2∙x∙x∙x 2∙x∙x∙x 3) (4y) 2 means 4∙4∙y∙y 4∙4∙y∙y What is the difference in 2 and 3? ∙

Write the following in exponential form 4) 3∙3∙3∙3 = 3 4 = 3 4 5) 4∙4∙4 = 4 3 = 4 3 Are these the same? 3 4 =4 3 =

Multiplying is a quicker way to write repeated ________ Multiplying is a quicker way to write repeated ________Addition x + x + x = 3∙x x + x + x = 3∙x Exponents are a quicker way to write repeated______ Exponents are a quicker way to write repeated______multiplication y∙y∙y∙y = y 4 y∙y∙y∙y = y 4

Special Powers Squared : a base to the second power (squares have 2 dimensions: length and width) 6 2 : can be read “6 to the second power” or “6 squared” The area of the side of a square with a side of s is A = s 2 so.. A = s 2 so..means 4 2 (4 squared) = 16 we are talking about the area!!!! 4

Cubed: a base to the third power (cubes have 3 dimensions (length-width- height) (cubes have 3 dimensions (length-width- height) 53 :53 :53 :53 : can be read 5 cubed The Volume of a cube is V = S 3 so the volume of this cube is V =4 3 (4 cubed) or 64 4

Zero / Negative Exponents What is 7 0 ? What is 5 -1?

Zero Power Any number to the zero power =1 EX: 4 0 = 1 Ex: (2x) 0 = 1 Ex: (5x 2 y 3 z 8 ) 0 = 1

Negative Exponents Negative exponents make fractions (dividing by the base) Ex: 2 -1 = Ex: 4 -2 = Ex: 5 -3 =

Examples Evaluate 6) 7n 3 for n=2 7*2 3 7*8 7* ) (7n) 3 for n=2 (7*2) 3 (7*2)

8) 5x 2 -x for x=2 (simplify all fraction answers) 2x 2x 5* * *2 2* =

Associative property(1-4): Changes the grouping of the parenthesis when adding or multiplying APA APM (1 +2) +3 = 1+(2+3) 15*2*10 =15(2*10) (a+b)+c+d= a+(b+c)+d (a*2)*3 =a*(2*3)

Using commutative and associative property, write three equivalent expressions 9) (3x + 6) +y

Assignment 1-3/18/2-32 eoe, 36-39, /22-23/10-46 eoe