9.2 Negative and Zero
Exponents
Definition of Negative Exponents
Let a be a nonzero number and let n be a
positive integer
The expression a-n is the reciprocal of an.
a-n = 1
a≠0
1 = an
-n
n
a
a
Ex: 3-2 = 1 = 1
32 9
The negative exponent says the number
needs to be moved to the opposite location
and made positive.
If it’s negative in the numerator, it
belongs in the denominator position and
needs to be positive.
If it’s negative in the denominator, it
belongs in the numerator position and
needs to be positive.
Definition of Zero Exponent
Let a be a nonzero number and let n be
a positive integer
A nonzero number to the zero power is
ALWAYS 1!
a0 = 1
a
0
30 = 1
(x2y5)0 = 1
The expression 00 is undefined.
Simplify expressions:
Write with positive exponents.
1)
2-2 =
1 =
22
1
4
2) 20 = 1
3) (2x)-3 = 1
(2x)3
=
1 = 1
23 ∙ x3
8x3
Simplify expressions:
Write with positive exponents.
1)
(-5)-3 =
1 = - 1
(-5)3
125
2) 24 ∙ 4-3 = 24 ∙ 1 = 24 ∙ 1 = 3
43
3) -3-4 = 1 = - 1
4
-3
81
64
8
Simplify expressions:
Write with positive exponents.
1) -5m-3n-5 = - 53 5
mn
2)
(4-2)2 =
4(-2 ∙ 2)
=
4-4 =
1
1
=
4
4
256
Simplify expressions:
Write with positive exponents.
1) 3a-3b-2 = 33 2
ab
2)
(3-3)2 =
3(-3 ∙ 2)
=
3-6 =
1
1
=
6
3
729
Homework
page 409 #6-40 even
Study for fraction quiz tomorrow
Quiz corrections due Friday