1-5: Negative Exponents
What is a ​
Zero
Exponent​
?
What is a ​
Negative
Exponent​
?
0​
23​
=1
but x ≠ 0
-3 ​ 1
7​
= 73
= 17 ∙ 17 ∙
Any base number
raised to a ​
zero
exponent ​
is always
1.
1
7
Any
nonzero
number to the
negative exponent
is the multiplicative
inverse of the nth
power.
Example 1a:
Page 44
Write
each
expression using a 1. Get rid of the
positive exponent: negative exponent.
-2
7​
Example 1d:
Page 44
Write
each
expression using a
positive exponent:
-3
m​
Example 2e:
Page 44
Write
each
fraction
as an
expression using a
negative exponent
other than -1:
1
83
Example 2g:
Page 44
Write each fraction
as an expression
using a negative
exponent
other
than -1:
1
c5
3​ -3
5​
∙ 5​
Multiply
and
Divide
with
Negative
Exponents​
?
The product of
powers and the
quotient of powers
rule can be used to
multiply and divide
powers
with
negative numbers.
Example 3j:
Page 45
Simplify
expression:
-8​ 2
3​
∙ 3​
each 1. Change the
negative exponents
to positive.
2. Follow the rules
for Product of
Powers.
Example 3m:
Page 45
Simplify
expression:
each 1. Change the
negative exponents
to positive.
2. Follow the rules
for Quotient of
Powers.
b −4
b −7