February 14,
2014
Warm-UpIntro to Exponents, Monomials
& Scientific Notation
At the V6Math Site:
For Explanations, Learning Concepts:
* purplemath.com* wowmath.org For Practice Problems: * khanacademy.org * braingenie.ck12.com
Vocabulary & Formulas Section of Notebook
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Practice Problems
1. 72
2. (-8)2
3. (-9) 3
4. -24
5. -43
Introduction to Monomials: Exponents
Exponent Laws
Exponent Laws
Exponent Laws
Simplify to lowest terms:
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Write 32.500 in Scientific Notation
Scientific Notation
Scientific Notation
Write the following in Scientific Notation:
.00458
= 4.58 • 10 - 3
Scientific Notation
Scientific Notation
Scientific Notation
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:
*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.
Negative and Zero Exponents
Example 3
Step 1:
Step 2:
Step 3:
Negative and Zero Exponents
Example 4:
Step 1:
Negative and Zero Exponents
Step 2:
Step 3:
Step 4:
Step 5:
Step 6-7:
Practice Problems
Negative Exponents: Answers
Negative Exponents: Answers
Negative Exponents: Answers
Warm- Up Exercises1. 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
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
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
MonomialsDefinition: 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!
Monomials
Examples of Monomials:
Multiplying MonomialsWhen 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
Multiplying Monomials
Multiplying Monomials
Multiplying Monomials
Multiplying Monomials
Multiplying Monomials
Multiplying Monomials
Now, complete the rest of the problem.
Multiplying Monomials
Multiplying Monomials
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
Multiplying Monomials Answers, con't.
3. (4a2b2c3)3 (2a3b4c2)2
Raise the 1st
monomial to the (64a6b6c9) (4a6b8c4) 3rd power and the 2nd monomial to the 2nd power.
Multiply the coefficients and add the variables with like bases
= 256a12b14c13
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.
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!
Dividing MonomialsExample 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.
Dividing MonomialsPower of a Quotient Example 1
Power of a Quotient Example 2
Dividing Monomials
Dividing Monomials Practice Problems
Dividing Monomials Answer Key
Simplifying MonomialsProperties 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.
Simplifying Monomials
Example of Multiplying Monomials
Example of Dividing Monomials
Simplifying Monomials: Sample Problems
Simplifying Monomials: Sample Problems
Complete the next step:
Simplifying Monomials: Sample Problems
Now the next:
Try to complete the problem:
Simplifying Monomials: Sample Problems
Simplifying Monomials: Sample Problems
Practice Problems
Sample Problem AnswersProblem 1
Sample Problem AnswersProblem 2
• x ≤ 4 • 5 - 2
If 7 pencils cost $6.65, write the proportion to find the cost for 4 pencils.
7 = 4 6.65 x
= 6.65 x 4 / 7 = $3.80