The document focuses on the concept of integer exponents in algebra, including the evaluation and simplification of expressions with zero and negative exponents. It provides examples and patterns for understanding how negative and zero exponents operate, emphasizing the importance of rewriting expressions with only positive exponents. Additionally, it includes practice problems and a classwork assignment to reinforce the learned concepts.

1. Holt Algebra 1
7-1 Integer Exponents
Language Objective: I will be able to …
• Read, write, and listen about vocabulary, key
concepts, and examples
Lesson Objectives: I will be able to …
• Evaluate expressions containing zero and
integer exponents
• Simplify expressions containing zero and
integer exponents

2. Holt Algebra 1
7-1 Integer Exponents
You have seen positive exponents. Recall that to simplify 32
,
use 3 as a factor 2 times: 32
= 3  3 = 9.
But what does it mean for an exponent to be negative or 0?
You can use a table and look for a pattern to figure it out.
3125 625 125 25 5
 5
Power
Value
55
54
53
52
51
5–1
50
5–2
 5  5  5
When the exponent decreases by one, the value of the
power is divided by 5. Continue the pattern of dividing by 5.

3. Holt Algebra 1
7-1 Integer Exponents
Base
x
Exponent
Remember!
4
Pages 1 – 2

4. Holt Algebra 1
7-1 Integer Exponents
Example 1: Cooking Application
One cup is 2–4
gallons.
Simplify this expression.
gal is equal to
Page 2

5. Holt Algebra 1
7-1 Integer Exponents
Your Turn 1
A sand fly may have a wingspan up to 5–3
m.
Simplify this expression.
5-3
m is equal to
Page 2

6. Holt Algebra 1
7-1 Integer Exponents
Example 2: Zero and Negative Exponents
Simplify.
A. 4–3
B. 70
7º = 1
Any nonzero number raised to the zero
power is 1.
C. (–5)–4
D. –5–4
Page 3

7. Holt Algebra 1
7-1 Integer Exponents
Example 3: Evaluating Expressions
with Zero and Negative Exponents
Evaluate the expression for the given values of
the variables.
–2a0
b-4
for a = 5 and b = –3
Substitute 5 for a and –3 for b.
Evaluate expressions with
exponents.
Write the power in the
denominator as a product.
Evaluate the powers in
the product.
Simplify.
Page 4

8. Holt Algebra 1
7-1 Integer Exponents
Your Turn 3
Evaluate the expression for the given values of
the variables.
for a = –2 and b = 6
2
Substitute –2 for a and 6 for b.
Evaluate expressions with
exponents.
Write the power in the
denominator as a product.
Evaluate the powers in
the product.
Simplify.
Page 4

9. Holt Algebra 1
7-1 Integer Exponents
What if you have an expression with a negative
exponent in a denominator, such as ?
or Definition of a negative
exponent.
Substitute –8 for n.
Simplify the exponent on
the right side.
So if a base with a negative exponent is in a denominator, it
is equivalent to the same base with the opposite (positive)
exponent in the numerator.
An expression that contains negative or zero exponents is
not considered to be simplified. Expressions should be
rewritten with only positive exponents.

10. Holt Algebra 1
7-1 Integer Exponents
Simplify.
Example 4: Simplifying Expressions with
Zero and Negative Numbers
A. 7w–4
B.
Page 5

11. Holt Algebra 1
7-1 Integer Exponents
Your Turn 4
Simplify.
Page 5

12. Holt Algebra 1
7-1 Integer Exponents
Classwork
Assignment #1
• Holt 7-1 #2-3 5-6, 8-9, 11, 16-23