### Lesson 6.1

```6-1
6-1 Integer
IntegerExponents
Exponents
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Holt
McDougal
Algebra 1Algebra
Algebra11
Holt
McDougal
6-1 Integer Exponents
Warm Up
Evaluate each expression for the given
values of the variables.
1. x3y2 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
Objectives
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 32, use 3 as a factor 2 times: 32 = ???
VOCABULARY
EXPONENT
Positive exponents
3
BASE
Holt McDougal Algebra 1
5
6-1 Integer Exponents
ZERO OR NEGATIVE EXPONENTS
look for a pattern to figure it out.
Power 55 54 53 52
Value 3125 625 125 25
5
50 =
5
=1
5
5
−1
5
Holt McDougal Algebra 1
=
5
51
5–1
5–2
5
When the exponent
decreases by one, the
value of the power is
divided by 5.
5
1
1
= 1
5 5
50
5
−2
=
1
1
1
÷5=
= 2
5
25 5
6-1 Integer Exponents
VOCABULARY
1. Zero Exponents – Any nonzero number
raised to the zero power is 1.
Examples:
30 = 1
(−16)0 = 1
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:
1
1
=
2
3
9
3−2
=
−
1
=
Holt McDougal Algebra 1
2−4
1
1
=
=
4
2
16
6-1 Integer Exponents
Why “nonzero number” in the
previous definition?
0
0
= 0
−2
0
=
Holt McDougal Algebra 1
1
1
= =
2
0
0
6-1 Integer Exponents
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
Simplify.
A. 4–3
B. 70
TRY THESE YOURSELF!!!
7º = 1
C. (–5)–4
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.
–2a0b-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.)
Holt McDougal Algebra 1
for a = –2 and b = 6
6-1 Integer Exponents
What if you have an expression with a negative
exponent in a denominator, such as
?
1
−
=

*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
Holt McDougal Algebra 1
B.
6-1 Integer Exponents
Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
C.
and
Holt McDougal Algebra 1
6-1 Integer Exponents
Simplify.
a. 2r0m–3
b.
Holt McDougal Algebra 1
c.
6-1 Integer Exponents
6.1 HOMEWORK
PG. 395 - 397
#24-42(all), 44-66(evens),
78-83, 100
Holt McDougal Algebra 1
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