Download Model Notes: Exponents Parts of a Power 2 3 3: power 2: base We

Model Notes: Exponents
Parts of a Power
23
3: power
2: base
We say: 2 to the power of 3
It means, 2 multiplied by itself 3 times, or 2 x 2 x 2 = 8
8 = standard form
2 x 2 x 2 = factored form
e.g.
33
_____: power
_____: base
We say: ____ to the power of _____
It means, _______ multiplied by itself ______ times,
Or ______________________
_____: standard form
2 x 2 x 2 = factored form
Exponents
An EXPONENT is the number of times a base is multiplied
by itself.
Exponents are short ways to write large numbers.
e.g. A short way to write 10 x 10 x 10 x 10 = 104
Note the pattern:
1000 = 10 x 10 x 10 = 103
100 = 10 x 10 = 102
10 = 10 x 1 = 101
1 = 100
4 563 = 4 x 103 + 5 x 102 + 6 x 10 + 3 x 1
(This is expanded form)
A POWER is a number raised to an exponent. Powers are
named by their bases.
5
6
If a power does not have an exponent, then an
exponent of 1 is assumed. Ex. 5 = 51
Exponential Form is a number written in the form of
a power. Ex. 54
Expanded Form is the number written as repeated
multiplication. Ex. The power 54 is expressed in
expanded form as 5 x 5 x 5 x 5.
Standard Form is the answer to a repeated
multiplication sentence. Ex. The power 54 expressed
in standard form is 625.
Negative exponents
The negative sign means: find the inverse of the
number, or, divide one by the number
e.g. 4 -1 = 1/41
In decimal form, the -1 tells us that the 4 is the first
digit after the decimal.
When the base is 10, it is simpler
10 -1 = or 0.1
Can you see a pattern?
10-1 = 0.1 =
10-2 =
=
10-3 =
=
What would 10-4 be?
Scientific Notation
Is a condensed way of writing very large or very
small numbers. Ex. 12 500 000
They look like this:
1.25 x 107
Converting Standard Form to Scientific Notation for
LARGE NUMBERS
1. Identify where the decimal is. This is the starting
point. If there is not a decimal, it is at the end of
the number.
2. Identify where the decimal needs to be (one nonzero digit in the front). This is the end point.
3. Count left the number of spaces from start to
end. The number of times the decimal is moved
to the left represents the exponent. The
exponent is positive to show that the number is
greater than 1.
4. Write out in scientific notation the new decimal
multiplied by a power of 10 (drop all of the
zeros).
Let’s try:
12 500 000
Going from Scientific Notation to Standard Form
for LARGE NUMBERS
Steps:
1. Identify where the decimal is. Starting Point!
2. Move the decimal to the right as many times as
the exponent. END POINT!
3. Fill in the empty spaces with zeros.
4. Rewrite the number properly
Ex. 3.82 x 107
3.8200000
Converting Standard Form to Scientific Notation for
SMALL NUMBERS
Steps:
1. Identify where the decimal is. This is the starting
point.
2. Identify where the decimal needs to be (one nonzero digit in the front). This is the end point.
3. Count right the number of spaces from start to
end. The number of times the decimal is moved
to the right represents the exponent. The
exponent is negative to show that the number is
smaller than 1.
4. Write out in scientific notation the new decimal
multiplied by a power of 10 (drop all of the
zeros).
Let’s try:
0.000 00125
Going from Scientific Notation to Standard Form
for SMALL NUMBERS
Steps:
1. Identify where the decimal is. Starting Point!
2. Move the decimal to the left as many times as
the exponent. END POINT!
3. Fill in the empty spaces with zeros.
4. Rewrite the number properly
Ex. 3.82 x 10-7
0.000000382
Seatwork Exponents
Name:
Complete the table
Power/Exponential
Form
24
Base
3
Exponent
Expanded
Form
Standard
Form
3
7
343
6x6
8
2
2
-4
3-2
0.01
¼
10
0
10
1
Write each product in exponential form:
4x4x4x4x4
______________
(3 x 3 x 3) x (3 x 3) _________________
Write as a power of 10:
100 ______________
1 000 000 _________________
10 000 _____________
0.001 _____________________
Write each number in scientific notation:
a) 5 163 000 000
b) 34.52
c) 0.000 000 000 203 4
d) 0.000 400 000 1
Write each number in standard form:
a) 43.232 x 1012
b) 1.314 792 x 104
c) 1.2 x 10-5
d) 5.62 x 10-12
Adding and Subtracting Exponents
Adding Exponents only happens when we are multiplying powers with the same
base….
(x3)(x4)
This means: (xxx)(xxxx) = x7
(x2)(x5)
This means: (xx)(xxxxx) = x7
Notice a pattern?
When we multiply two terms with the same base, we add the exponents!
Eg. (x2)4 =
(x2)(x2)(x2)(x2)
(xx)(xx)(xx)(xx)
xxxxxxxx
x8
x(2x4)
Whenever you have an exponent expression that is raised to a power, you can multiply
the exponent and power
Subtracting Exponents only happens when we are dividing powers with the same
base….
X6 divided by x3 = x(6-3) = x3
When we divide two terms with the same base, we subtract the exponents!
***You can only take this short cut if you are:
 Multiplying
 Dividing
 The bases are the same.