Algebra 1 Common Core Student Edition, Grade 8-9

Zero and N eg at ive

Ex p o n e n t s

®cbmmon Core State Standards

Pr ep ar es f o r N-RN.A.1 Explain how the defin ition

o f the meaning o f rational exponents fo llo w s from

extending the properties o f integer exponents to those

values... Also prepares f or N-RN.A.2

MP 1, MP 2, MP 3, MP 4, MP 7

Object ive To simplify expressions involving zero and negative exponents

Lo o k f o r a p a t t e r n

in t he values in t he

table.

MATHEMATICAL

PRA CTI CES

eS>VVf^ r -............................

Get t i n g Read y!

Co p y an d co m p l e t e t h e t a b l e. M ak e a

co nject ure about how t he value o f an

exponent ial exp ressio n (an exp ressio n

cont aining an exp o nent ) changes when

you d ecrease t h e exponent b y 1.

What do you think the value of 5 2 is?

Explain your reasoning.

2* 10x

24 = 8

• 10= 8.....................-4
  23 = 8 103 = 8
  22 102 = 8
  21 =

..................... ^

101 = B

2 0 = 8 10° = 8

2 ~1 = a __10“ 1 = 8______

2” 2 = 8 ; OIhoII

The patterns you found in the Solve It illustrate the definitions of zero and negative

exponents.

Esse n t i a l U n d e r st a n d i n g You can extend the idea of exponents to include zero

and negative exponents.

Consider 33, 32, and 31. Decreasing the exponents by 1 is the same as dividing by 3. If

you continue the pattern, 3 equals 1 and 3 equals -l 3.

Pro p ert ies Zero and Negative Exponents

Zero as an Exp o n en t For every nonzero number a, a° = 1.

Ex a m p l e s 4° = 1 (-3)° = 1 (5.14)° = 1

Negative Exponent For every nonzero number a and integer n, a ” =

73

Ex a m p l e s 7~3 = -3 (—5l-2 = — -—

1 J (-5)2

418 Ch ap t er 7 Ex p o n e n t s a n d Ex p o n e n t i a l Fu n c t i o n s