2. At the V6Math Site:
For Explanations, Learning Concepts:
* purplemath.com* wowmath.org
For Practice Problems:
* khanacademy.org
* braingenie.ck12.com
28. Negative and Zero Exponents
Take a look at the following problems and see if you
can find the pattern.
The expression a-n is the reciprocal of an
Examples:
29. Negative and Zero Exponents
*Any number (except 0) to the zero power is equal to 1.
Negative Exponents
Example 1
Example 2
Since 2/3 is in parenthesis, we must apply the power of a
quotient property and raise both the 2 and 3 to the negative
2 power. First take the reciprocal to get rid of the negative
exponent. Then raise (3/2) to the second power.
38. Warm- Up Exercises
1. A board 28 feet long is cut into two pieces. The ratio of
the lengths of the pieces is 5:2. What are the lengths of
the two pieces?
5:7 = X:28; x1 = 20 ft., x2 = 8 feet.
2. The ratio of the length to the width of a rectangle is 5:2.
The width is 24 inches long. Find the length.
5:2 = x: 24; Length = 60"
3. What is: 5 6 • 5 - 2
= 5 4 ; 625
39. Warm- Up Exercises
4.
(12) -5 • (12) 3
Since the bases are the same (12): the exponents are
added. -5 + 3 = -2; (12)-2 = 1/12 2 = 1/144
5.
42 • 35 • 24
43 • 35 • 22
=
22
4
=1
6. Simplify: 5b • 6a4
a
c
= 30ba4 c
48. Monomials
Definition: Mono-- The prefix means one.
A monomial is an expression with one term.
In the equations unit, we said that terms were separated
by a plus sign or a minus sign!
Therefore:
A monomial CANNOT contain a plus sign (+) or a
minus (-) sign!
50. Multiplying Monomials
When you multiply monomials, you will
need to perform two steps:
•Multiply the coefficients (constants)
•Multiply the variables
A simple problem would be: (3x2)(4x4)
And the answer is:
12x6 Remember, the bases
are the same, so you add the exponents
59. Multiplying Monomials Answers
1. (3x5y 2 ) (-5x3y 6 )
Multiply the coefficients. Then multiply the variables (add
the exponents of like variables).
-15x 8 y 8
2.(-2r3s7t4 )2 (-6r2t 6)
Raise the 1st monomial to the 2nd power.
(4r6s14t8) (-6r2t 6): Multiply the coefficients and add the
variables with like bases
= -24r 8s14 t14
60. Multiplying Monomials Answers, con't.
3. (4a2b2c3)3 (2a3b4c2)2
the (64a6b6c9) (4a6b8c4)
Raise the 1st monomial to
3rd power and the 2nd
monomial to the 2nd power.
Multiply the coefficients and add the variables with like
bases
= 256a12b14c13
61. Dividing Monomials
As you've seen in earlier examples, when we work
with monomials, we see a lot of exponents.
Hopefully you now know the laws of exponents
and the properties for multiplying exponents, but
what happens when we divide monomials? You
probably ask yourself that question everyday.
62. Dividing Monomials
Expanded Form Examples
When you divide powers that have the same base, you subtract the
exponents. That's a pretty easy rule to remember. It's the opposite of
the multiplication rule. When you multiply powers that have the
same base, you add the exponents and when you divide powers that
have the same base, you subtract the exponents!
63. Dividing Monomials
Example 1
Example 2
That's an easy rule to remember. Let's look at one more
property. The Power of a Quotient Property. A Quotient is an
answer to a division problem. What happens when you raise a
fraction (or a division problem) to a power? Remember: A
division bar and fraction bar are the same thing.
67. Simplifying Monomials
Properties of Exponents and Using the Order of Operations
• If you have a combination of monomial expressions
contained with in grouping symbols (parenthesis or
brackets), these should be evaluated first.
• Power of a Power Property - (This is similar to evaluating
Exponents in the Order of Operations). Always evaluate a
power of a power before moving on the problem.
Example of Power of a Power:
• When you multiply monomial expressions, add the
exponents of like bases.
