Negative Exponents

1
X-5
Negative Exponents 8.2
SWBAT simplify expressions with negative and zero
exponents
2
Warm Up

• Can you find the pattern?
• What comes next?
• X3 . X4 X7
• X4 . X3 X7
• X5 . X2 X7
• X6 . X1 X7
• X7. X0 X7

3
We found X8 . X-1 X7
What is a negative exponent telling us? X-1
4
Consider this Pattern
81 / 3 27
34 81 33 27 32 9 31 3 30 1
27 / 3 9
9 / 3 3
3 / 3 1
What do you notice?
What do you think comes next?
5
30 1 3-1 1/3
Lets keep going
3-2 ? 3-3 ? 3-4 ?
6
Negative Exponent Property
For any nonzero b and all n,
b-n 1 bn
7
Examples
Write each of the following without negative
exponents
1.) 3-3 2.)4-y 3.) a6 . b-7 4.)
(1/3)-1 5.) 0 1 6.) 4(3-k)
8
What about this?
How can I write this with no negative exponents?
(2x5)-3 ?
9
More Examples
10
What about a zero power?
What is any number but zero raised to the 0
power? x0 __?__ x?0
x0 __1__ x?0
Example 32 3-2
11
Homework Page 459 2 14-36 even 37- 45 all