Download 7-1 Integer Exponents

7-1 Integer Exponents
Bellringer
Evaluate each expression for the given
values of the variables.
1. x3y2 for x = –1 and y = 10 -100
2.
for x = 4 and y = (–7) 48/49
Write each number as a power of the
given base.
3
3. 64; base 4 4 = 64
4. –27; base (–3) (-3)3 = 27
Holt Algebra 1
7-1 Integer Exponents
Know:
Objectives
Evaluate expressions containing zero and integer
exponents.
Simplify expressions containing zero and integer
exponents.
Evaluate and multiply by powers of 10.
Convert between standard notation and scientific notation.
Do:
Write in Scientific notation
0.00000123
2.1.2 generates and explains a pattern.
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
Holt Algebra 1
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.
Holt Algebra 1
7-1 Integer Exponents
Remember!
Base
x4
Exponent
Holt Algebra 1
7-1 Integer Exponents
In Your Notes
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.
Holt Algebra 1
7-1 Integer Exponents
Reading Math
2–4 is read ―2 to the negative fourth power.‖
Holt Algebra 1
7-1 Integer Exponents
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
Holt Algebra 1
7-1 Integer Exponents
Caution
In (–3)–4, the base is negative because the
negative sign is inside the parentheses. In –3–4
the base (3) is positive.
Holt Algebra 1
7-1 Integer Exponents
Simplify.
In Your Notes
Check It Out! Example 2
a. 10–4
b. (–2)–4
c. (–2)–5
d. –2–5
Holt Algebra 1
7-1 Integer Exponents
In Your Notes
Check It Out! Example 3a
Evaluate the expression for the given value of
the variable.
p–3 for p = 4
Substitute 4 for p.
Evaluate exponent.
Write the power in the
denominator as a product.
Evaluate the powers in
the product.
Holt Algebra 1
7-1 Integer Exponents
In Your Notes
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.
Evaluate expressions with
exponents.
2
Holt Algebra 1
Write the power in the
denominator as a product.
Evaluate the powers in
the product.
Simplify.
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.
Holt Algebra 1
7-1 Integer Exponents
In Your Notes
Check It Out! Example 4
Simplify.
a. 2r0m–3
rº = 1 and
b.
Holt Algebra 1
c.
.
7-1 Integer Exponents
Holt Algebra 1
7-1 Integer Exponents
Holt Algebra 1
7-1 Integer Exponents
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.
Holt Algebra 1
7-1 Integer Exponents
In Your Notes
Holt Algebra 1
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.
Holt Algebra 1
7-1 Integer Exponents
In Your Notes
Check It Out! Example 1
Find the value of each power of 10.
a. 10–2
b. 105
c. 1010
Start with 1
and move the
decimal point
two places to
the left.
0.01
Start with 1
and move the
decimal point
five places to
the right.
100,000
Start with 1
and move the
decimal point
ten places to
the right.
10,000,000,000
Holt Algebra 1
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.
Holt Algebra 1
7-1 Integer Exponents
In Your Notes
Check It Out! Example 2
Write each number as a power of 10.
a. 100,000,000
b. 0.0001
c. 0.1
The decimal
point is eight
places to the
right of 1, so the
exponent is 8.
The decimal
point is four
places to the
left of 1, so the
exponent is –4.
The decimal
point is one
place to the
left of 1, so the
exponent is –1.
Holt Algebra 1
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
Holt Algebra 1
7-1 Integer Exponents
In Your Notes
Check It Out! Example 3
Find the value of each expression.
a. 853.4  105
853.4 0 0 0 0
85,340,000
Move the decimal point 5
places to the right.
b. 0.163  10–2
0.0 0163
0.00163
Holt Algebra 1
Move the decimal point 2
places to the left.
7-1 Integer Exponents
In Your Notes
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.
Holt Algebra 1
7-1 Integer Exponents
Reading Math
Standard form refers to the usual way that
numbers are written—not in scientific notation.
Holt Algebra 1
7-1 Integer Exponents
In Your Notes
Check It Out! Example 4a
Use the information above to write Jupiter’s
diameter in scientific notation.
143,000 km
143000
5 places
1.43  105 km
Holt Algebra 1
Count the number of places
you need to move the
decimal point to get a
number between 1 and 10.
Use that number as the
exponent of 10.
7-1 Integer Exponents
In Your Notes
Check It Out! Example 4b
Use the information above to write Jupiter’s
orbital speed in standard form.
13000
13,000 m/s
Holt Algebra 1
Move the decimal point 4 places to
the right.
7-1 Integer Exponents
In Your Notes
Check It Out! Example 5
Order the list of numbers from least to greatest.
Step 1 List the numbers in order by powers of 10.
2  10-12, 4  10-3, 5.2  10-3, 3  1014, 4.5  1014,
4.5  1030
Step 2 Order the numbers that have the same
power of 10
Holt Algebra 1
7-1 Integer Exponents
Holt Algebra 1
7-1 Integer Exponents
Daily Asn
7.1 & 7.2 Practice B Worksheets
Holt Algebra 1