Download Chapter 4 Exponents

Chapter 4
Notes 4-2
Exponents
Parts of an Exponent
the exponent tells HOW MANY times
Example
the base tells WHAT number
3² means 3 x 3 = 9
−2 • a • a • a • b = −2a³b
be careful of negatives (−2 )² = (−2 )(−2 ) = 4
but
− 2 ² = − ( 2 • 2 ) = −4
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Notes 4-7
Multiplying Exponents
To multiply exponents with the same base,
write the base and add the exponents.
To multiply exponents with different bases,
multiply the base and simplify the exponents.
Taking a Power
TO A POWER!
This means (a²) 4 times (a²)(a²)(a²)(a²) means a• a• a• a• a• a• a• a
multiply the exponents 2 x 4 = 8
=a
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Notes 4-8
Dividing Exponents
To divide exponents with the same base,
write the base and subtract the exponents.
You can also end up with only a denominator.
This can be written with a negative exponent
Anything to the (0) exponent = 1
(xy)
or on the bottom of a fraction.
2³ = 8
Follow the pattern.
Each answer is cut in half.
2² = 4
2¹ = 2
2° = 1
2
=½
2
=¼
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Notes 5-9 Powers of products and Quotients
To Raise a PRODUCT to a power - raise each factor to the power.
(5 · 3)³ = 5³ · 3³ = 125 · 27 = 3375
To Raise a QUOTIENT to a power - raise both parts to the power.
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Scientific Notation always has this form
Notes 4-9
One digit, a decimal, the rest of the number, X 10 to an exponent
For the exponent, count the spaces the decimal must move
to get to decimal to its right spot.
examples
6
2,000,000
=
2 X10
BIG numbers have a POSITIVE exponent.
-5
0.00004
=
4 X10
Little numbers have a NEGATIVE exponent.
STANDARD FORM is just a REGULAR NUMBER.