This document provides examples and explanations of operations involving exponents, including: 1) Simplifying expressions with integer exponents and evaluating expressions with fractional exponents. 2) Moving terms with negative exponents to the other side of a fraction by taking their reciprocal. 3) Rewriting expressions with negative exponents as expressions with only positive exponents.

1. Warm-upSession 17
Simplify each expression completely.
83
92
34
336
x.4
48.3
45.2
.1
xx
aab
xx
yx
918
yx
7
000,40 x
211
256 ba
12
x

2. Homework Check
You can use your anything in your notebook to help you, just not
your text book.
Write each expression as a single power of the
base.
1. 73 76
2. (y4)3
Simplify each expression.
3. (2y)4
4. (3b3)2 b
Turn this in on the cart.
Make sure your name is on your paper.

3. Zero & Negative Exponents

4. Negative exponents move terms to the other part of the
fraction. (reciprocal)
Example 1: Evaluate
x
y
2
4 x
y2
4
4 is downstairs.
We will move it…
x
y16

5. Example 2
4
3
x 1
3 4
x 4
3x
x is downstairs.
We will move it…

6. Example 3
2
9 2
9
1
81
1
-9 is upstairs.
We will move it…

7. Now let’s include what we learned from last class.
33
44 33
4 0
4 1
42
3 8
3 6561
What do we know that we can do
with these exponents?
What do we know that we can do with these
exponents?
2
25 2
10 2
)10(
1
100
1

8. Evaluate the expression without using a calculator.
2
21
32
43.6
3.5
44.4
-
4
1
9
144
1

9. Rewrite the expression with positive exponents.
3
2
33
5.9
3
.8
2.7
b
x
yx
3
3
2
x
y
2
3x
3
125
1
b