Feb. 14th, 2014

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