6-1 Integer Exponents
Warm Up
Lesson Presentation
Lesson Quiz

6-1 Integer Exponents
Warm Up
Evaluate each expression for the given values of the variables.
1. x 3 y 2 for x = –1 and y = 10
2.
for x = 4 and y = (–7)
Write each number as a power of the given base.
3. 64; base 4
4. –27; base (–3)
Holt McDougal Algebra 1

6-1 Integer Exponents
Evaluate expressions containing zero and integer exponents.
Simplify expressions containing zero and integer exponents.
Holt McDougal Algebra 1

6-1 Integer Exponents
RECALL:
Positive exponents.
To simplify 3 2 , use 3 as a factor 2 times: 3 2 = ???
VOCABULARY
EXPONENT
Positive exponents
5 3
BASE
Holt McDougal Algebra 1

6-1 Integer Exponents
ZERO OR NEGATIVE EXPONENTS look for a pattern to figure it out.
5
Power
Value
5 5 5 4 5 3 5 2 5 1
3125 625 125 25 5
0 =
5
5
= 1
 5
5
 5  5  5
−1 =
1
5
1
=
5 1
5 0 5 –1 5 –2
5
When the exponent decreases by one, the value of the power is divided by 5.
−2 =
1
5
÷ 5 =
1
25
=
1
5 2
Holt McDougal Algebra 1

6-1 Integer Exponents
VOCABULARY
1. Zero Exponents – Any nonzero number raised to the zero power is 1.
Examples:
3 0 = 1
(−16) 0 = 1 𝑥 0 = 1
Holt McDougal Algebra 1

6-1 Integer Exponents
VOCABULARY
2. Negative Exponents– A nonzero number raised to a negative exponent is equal to 1 divided by that number raised to the opposite (postive) exponent.
Example:
3 −2 =
1
3 2
=
1
9
1 𝑥 −𝑛 = 𝑥 𝑛
Holt McDougal Algebra 1
2 −4 =
1
2 4
1
=
16

6-1 Integer Exponents
Why “nonzero number” in the previous definition?
0 0 = 0
0 −2 =
1
0 2
=
1
0
= 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
Holt McDougal Algebra 1

6-1 Integer Exponents
Reading Math
2 –4 is read “2 to the negative fourth power.”
Holt McDougal Algebra 1

6-1 Integer Exponents
Example 1: Application
One cup is 2 –4 gallons. Simplify this expression.
gal is equal to
Holt McDougal Algebra 1

6-1 Integer Exponents
Try this one yourself!!!
A sand fly may have a wingspan up to 5 –3 m.
Simplify this expression.
Holt McDougal Algebra 1

6-1 Integer Exponents
TRY THESE YOURSELF!!!
Simplify.
A. 4 –3
B. 7 0
C. (–5) –4
7º = 1
D. –5 –4
E. (–2) –5
Holt McDougal Algebra 1

6-1 Integer Exponents
Caution
In (–5) –4 , the base is negative because the negative sign is inside the parentheses. In –5 –4 the base (5) is positive.
Holt McDougal Algebra 1

6-1 Integer Exponents
Example 2
Evaluate the expression for the given value of the variables.
x –2 for x = 4
Substitute 4 for x.
Use the definition
Holt McDougal Algebra 1

6-1 Integer Exponents
Example 3: Try another yourself!!!
Simplify the expression for the given values of the variables.
–2a 0 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.
Simplify the denominator.
Simplify.
Holt McDougal Algebra 1

6-1 Integer Exponents
Try these yourself!!!
Evaluate the expression for the given value of the variable.
1.) p –3 for p = 4
2.) for a = –2 and b = 6
Holt McDougal Algebra 1

6-1 Integer Exponents
What if you have an expression with a negative exponent in a denominator, such as ?
1 𝑥 −𝑛
= 𝑥 𝑛
*Move the denominator to the top and change the sign
**An answer with a negative exponent
IS NOT simplified fully
Holt McDougal Algebra 1

6-1 Integer Exponents
Example 4: Together
Simplify.
A. 7w –4 B.
Holt McDougal Algebra 1

6-1 Integer Exponents
Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
C.
and
Holt McDougal Algebra 1

6-1 Integer Exponents
PRACTICE: ON YOUR OWN
Simplify.
a. 2r 0 m –3 b.
c.
Holt McDougal Algebra 1

6-1 Integer Exponents
6.1 HOMEWORK
PG. 395 - 397
#24-42(all), 44-66(evens),
78-83, 100
Holt McDougal Algebra 1