Algebra 1 Common Core Student Edition, Grade 8-9

Think

Can y o u u se t h e

d ef init ion of zero as

an ex p o n en t w h en

t he b ase is a n eg at ive

number?

Ye s, t h e d e f i n i t i o n o f ze r o

as an exponent is t rue f or

al l nonzero bases.

Which part of the
expression do you
need to rewrite?
Th e b ase b has a negative
exponent , so you need t o
rewrite it with a positive
exponent.

Why can’t you use 0 as a base with zero exponents? The first property on the previous

page implies the following pattern.

3° = 1 2° = 1 1° = 1 0° = 1

However, consider the following pattern.

03 = 0 02 = 0 01 = 0 0 ° = 0

It is not possible for 0° to equal both 1 and 0. Therefore 0° is undefined.

Why can't you use 0 as a base with a negative exponent? Using 0 as a base with a

negative exponent will result in division by zero, which is undefined.

Si m p l i f y i n g P o w e r s

What is the simplified form of each expression?

Or 2

9 — 9 = -^1 t Use the definition of negative exponent.

= Simplify.

0 ( - 3 .6 ) ° = 1 Use the definition of zero as an exponent.

An algebraic expression is in simplest form when powers with a variable base are

written with only positive exponents.

Si m p l i f y i n g Ex p o n e n t i a l Ex p r e ssi o n s

What is the simplified form of each expression?

Q 5a 3b ~ 2

5 a3b~2 = 5a3|y-:j Use t he definit ion o f negat ive exponent.

Csj 3

= -g£ Simplify.

X D

Xzy = 1 -r x~5 Rewrite using a division symbol.

= 1 h- Use the definition of negative exponent.

= 1 • xs Multiply by the reciprocal of which is x5.

= x5 Identity Property of Multiplication

Go t It? 2. What is the simplified form of each expression?

a. x-9 b. -z? n 3 c. 4c-3b d. -zj a 3 e.mz

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