Transcript Document

Warm Up
Evaluate each expression for the given
values of the variables.
1. x3y2 for x = –1 and y = 10
2.
–100
for x = 4 and y = (–7)
Write each number as a power of the
given base.
3. 64; base 4
43
4. –27; base (–3)
(–3)3
Objectives
Evaluate expressions containing zero
and integer exponents.
Simplify expressions containing zero
and 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.
Power 55 54 53 52
Value 3125 625 125 25
5
5
5
5
51
5
50
5–1
5–2
When the exponent decreases by one, the value
of the power is divided by 5. Continue the
pattern of dividing by 5.
Remember!
Base
x
4
Exponent
Notice the phrase “nonzero number” in the
previous table. This is because 00 and 0 raised to
a negative power are both undefined. For
example, if you use the pattern given above the
table with a base of 0 instead of 5, you would
get 0º =
. Also 0–6 would be
=
. Since
division by 0 is undefined, neither value exists.
Reading Math
2–4 is read “2 to the negative fourth power.”
Example 1: Application
One cup is 2–4 gallons. Simplify this expression.
gal is equal to
Check It Out! Example 1
A sand fly may have a wingspan up to 5–3 m.
Simplify this expression.
5-3 m is equal to
Example 2: Zero and Negative Exponents
Simplify.
A. 4–3
B. 70
7º = 1
C. (–5)–4
D. –5–4
Any nonzero number raised to the zero
power is 1.
Caution
In (–3)–4, the base is negative because the
negative sign is inside the parentheses. In –3–4
the base (3) is positive.
Simplify.
a. 10–4
Check It Out! Example 2
b. (–2)–4
c. (–2)–5
d. –2–5
Example 3A: Evaluating Expressions with Zero and
Negative Exponents
Evaluate the expression for the given value of the
variables.
x–2 for x = 4
Substitute 4 for x.
Use the definition
Example 3B: Evaluating Expressions with Zero and
Negative Exponents
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.
Check It Out! Example 3a
Evaluate the expression for the given value of
the variable.
p–3 for p = 4
Substitute 4 for p.
Simplify exponent.
Write the power in the
denominator as a product.
Simplify the denominator.
Check It Out! Example 3b
Evaluate the expression for the given values
of the variables.
for a = –2 and b = 6
Substitute –2 for a and 6 for b.
Simplify expressions with
exponents.
Write the power in the
denominator as a product.
Simplify the denominator.
2
Simplify.
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.
An ifexpression
that
contains exponent
negative or
zero
So
a base with
a negative
is in
a
exponents is it
not
to the
be simplified.
denominator,
is considered
equivalent to
same base with
Expressions
be exponent
rewritten with
positive
the
opposite should
(positive)
in theonly
numerator.
exponents.
Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
A. 7w–4
B.
Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
C.
and
Check It Out! Example 4
Simplify.
a. 2r0m–3
rº = 1 and
b.
c.
.
Lesson Quiz: Part I
1. A square foot is 3–2 square yards. Simplify this
expression.
Simplify.
2. 2–6
3. (–7)–3
4. 60
5. –112
1
–121
Lesson Quiz: Part II
Evaluate each expression for the given
value(s) of the variables(s).
6. x–4 for x =10
7.
for a = 6 and b = 3