Transcript 5 Holt Algebra 1 7-1

7-1 Integer Exponents
Objectives
Evaluate expressions containing zero
and integer exponents.
Simplify expressions containing zero
and integer exponents.
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.
Power 55 54 53 52
Value 3125 625 125 25
5
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5
5
5
51
5
50
5–1
5–2
7-1 Integer Exponents
When the exponent decreases by one, the value
of the power is divided by 5. Continue the
pattern of dividing by 5.
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7-1 Integer Exponents
Remember!
Base
x
4
Exponent
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7-1 Integer Exponents
Holt Algebra 1
7-1 Integer Exponents
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.
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7-1 Integer Exponents
Reading Math
2–4 is read “2 to the negative fourth power.”
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7-1 Integer Exponents
Example 1: Application
One cup is 2–4 gallons. Simplify this expression.
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7-1 Integer Exponents
Your Turn 1
A sand fly may have a wingspan up to 5–3 m.
Simplify this expression.
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Example 2: Zero and Negative Exponents
Simplify.
A. 4–3
B. 70
C. (–5)–4
D. –5–4
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7-1 Integer Exponents
Simplify.
a. 10–4
b. (–2)–4
c. (–2)–5
d. –2–5
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Your Turn 2
7-1 Integer Exponents
Example 3A: Evaluating Expressions with Zero and
Negative Exponents
Evaluate the expression for the given value of the
variables.
x–2 for x = 4
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7-1 Integer Exponents
Example 3B: Evaluating Expressions with Zero and
Negative Exponents
Evaluate the expression for the given values of
the variables.
–2a0b-4 for a = 5 and b = –3
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7-1 Integer Exponents
Your Turn 3a
Evaluate the expression for the given value of
the variable.
p–3 for p = 4
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7-1 Integer Exponents
Your Turn 3b
Evaluate the expression for the given values
of the variables.
for a = –2 and b = 6
2
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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.
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.
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7-1 Integer Exponents
Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
A. 7w–4
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B.
7-1 Integer Exponents
Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
C.
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7-1 Integer Exponents
Your Turn 4
Simplify.
a. 2r0m–3
b.
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c.
7-1 Integer Exponents
Objectives
Evaluate and multiply by powers of 10.
Convert between standard notation and
scientific notation.
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7-1 Integer Exponents
Vocabulary
scientific notation
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The table shows relationships between several
powers of 10.
Each time you divide by 10, the exponent decreases
by 1 and the decimal point moves one place to the
left.
Holt Algebra 1
7-1 Integer Exponents
The table shows relationships between several
powers of 10.
Each time you multiply by 10, the exponent
increases by 1 and the decimal point moves one
place to the right.
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7-1 Integer Exponents
Holt Algebra 1
7-1 Integer Exponents
Example 1: Evaluating Powers of 10
Find the value of each power of 10.
A. 10–6
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B. 104
C. 109
7-1 Integer Exponents
Writing Math
You may need to add zeros to the right or left of
a number in order to move the decimal point in
that direction.
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7-1 Integer Exponents
Your Turn 1
Find the value of each power of 10.
a. 10–2
0.10
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b. 105
1,000,000
c. 1010
100,000,000,000
7-1 Integer Exponents
Reading Math
If you do not see a decimal point in a number, it
is understood to be at the end of the number.
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7-1 Integer Exponents
Example 2: Writing Powers of 10
Write each number as a power of 10.
A. 1,000,000
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B. 0.0001
C. 1,000
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Your Turn 2
Write each number as a power of 10.
a. 100,000,000
107
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b. 0.0001
10-5
c. 0.1
10-2
7-1 Integer Exponents
You can also move the decimal point to find the
value of any number multiplied by a power of 10.
You start with the number rather than starting with
1.
Multiplying by Powers of 10
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Example 3: Multiplying by Powers of 10
Find the value of each expression.
A. 23.89  108
B. 467  10–3
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Your Turn 3
Find the value of each expression.
a. 853.4  105
85,340,000
b. 0.163  10–2
0.00163
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7-1 Integer Exponents
Scientific notation is a method of writing numbers
that are very large or very small. A number written
in scientific notation has two parts that are
multiplied.
The first part is a number that is greater than or equal
to 1 and less than 10.
The second part is a power of 10.
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7-1 Integer Exponents
Example 4A: Astronomy Application
Saturn has a diameter of about
Its distance from the Sun is about
1,427,000,000 km.
km.
Write Saturn’s diameter in standard form.
Write Saturn’s distance from the Sun in
scientific notation.
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7-1 Integer Exponents
Reading Math
Standard form refers to the usual way that
numbers are written—not in scientific notation.
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7-1 Integer Exponents
Example 5: Comparing and Ordering Numbers in
Scientific Notation
Order the list of numbers from least to greatest.
Step 1 List the numbers in order by powers of 10.
Step 2 Order the numbers that have the same
power of 10
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7-1 Integer Exponents
Your Turn Example 5
Order the list of numbers from least to greatest.
Step 1 List the numbers in order by powers of 10.
Step 2 Order the numbers that have the same
power of 10
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Homework
Pg. 449: 24 – 57 odd
Pg. 455: 14 – 35 odd
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