Algebra 1 Chapter 7 Notes

Chapter 7: Exponents

Notes #1: Sections 7.1 and 7.2

Section 7.1: Review

Simplify; leave all answers in positive exponents:

1.) m-32.) y-13.) 6m0 4.) 2-3

5.) 4-26.) -3-37.) (7m4)08.)

Evaluate if a = -2 and b = -3:

9.) a2b-110.) 2ab-111.) a-1 + b-112.) (ab)-2

Section 7.2: Scientific Notation

A. Why Scientific Notation?

Compare:145,000,000 vs 1.45 x 1080.00000023 vs 2.3 x 10-7

Why do we use scientific notation?When will it be used most often?

B. Format for Scientific Notation

Examples: -2.7 x 10-3 3.081 x 1011

Is each number written in scientific notation? If no, explain.

1.) 35 x 1072.) -3.903 x 1013.) -12 x 100.5

C. Writing in Standard Notation

Converting from Scientific Notation to Standard Notation
•If 10 is to a ______power, move the decimal that many places to the ______
•If 10 is to a ______power, move the decimal that many places to the ______

Write in standard notation:

4.) 2.35 x 103 5.) -1.4 x 10-4 6.) 9.876 x 10-67.) -5.61 x 108

D. Writing in Scientific Notation

Converting from Standard Notation to Scientific Notation
•Place the decimal point so that you have 1 digit to the left of the decimal point
___. ______
•Count the number of places you need to move the decimal to get back to your original number. This number will be the exponent on the 10.
•If you are moving to the left, this exponent will be ______
•If you are moving to the right, this exponent will be ______

Write in scientific notation:

8.) -8739.) 13,000 10.) 0.006311.) -0.05

12.) 125.7 x 10813.) 0.045 x 10-714.) 42.301 x 10-3

15.) 0.000375 x 10816.) 3(1.2 x 109)17.) 3(4.5 x 105)

18.) 0.5(1.8 x 10-9)19.) 0.5(12.7 x 103)20.) 5.2(4.2 x 10-2)

21.) 3.1(0.00004)22.) 4.5(-5.3 x 108)23.) (45,000)(123)

Order the numbers from least to greatest:

24.) 0.052 x 107, 5.12 x 105, 53.2 x 10 and 53425.) 60.2 x 10-5, 63 x 104, 0.067 x 103, 61 x 10-2

Notes #2: Section 7.3

Section 7.3

A. Writing Expressions with Exponents

Simplify. Express each in exponential form:

1.) 2.) 3.)

4.) x2·x5·x·x35.) y3·y2·y4·y6.) 3·m4·2·m2·m

What pattern did you notice with the exponents?

B. Multiplying Monomials

Multiplying Monomials
When I multiply variable expressions together, I ______the coefficients
AND
I ______the exponents of terms with the same base.

Simplify each expression. Leave answers with positive exponents.

7.) (-3m-2n5)(2mn2)8.) (-4p3q)(-5p2q-6)9.) (9x-3y2z)(-3x-4yz)

10.) 35 ∙ 3-2 ∙ 3711.) 34 ∙ 22 ∙ 3-312.) (3c6)(c-2d8)(-2cd-5)

C. Applications to Scientific Notation

Multiplying Numbers in Scientific Notation
  • Multiply Coefficients (decimal terms)
  • Add Exponents
  • Check to make sure that the answer is in scientific notation

13.) (2.5 x 105)(3.0 x 108)14.) (1.6 x 10-3)(3.0 x 105)

15.) (5.4 x 10-2)(6.2 x 10-6)16.) (9.3 x 10-4)(3.1 x 105)

17.)(8.4 x 10-7)(3.6 x 10-3)18.) (-7.3 x 10-4)(9.1 x 108)

D. Other Applications

Complete each equation (fill-in-the-blank with a number)

17.) 18.)

19.) 20.) x4y( ) ∙ x( ) = y2

E. Comparing Addition and Multiplication

21.) (4x2)(5x2) vs. 4x2 + 5x222.) (7y3)(5y3) vs. 7y3 + 5y3

23.) (14b2)(3b3) vs. 14b2 + 3b324.) (7n5)(3n4) vs. 7n5 + 3n4

Combine like terms:

25.) 7m – 3n + 6n – 8m 26.) 3x2 – 7x + 8x2 – 2x27.) 3ab4– 2ab3 + ab4+ 8ab2

28.) 6j3k2 – 7j3k2+ 8jk – jk 29.) 19w8z3 – 8w7z2 + 11w8z330.) 10x4y3z – 2x4y3z2 + 4x4y3z

Notes #3: Section 7.4

A. Raising a Power to a Power

Explore:

1.) (x2)4 versus (x2)(x4)2.) (3y3)2 versus 2(3y2)

Raising a Power to a Power
  • Raise the coefficient to the power; evaluate
  • ______the exponents on the variables

Simplify; leave in terms of positive exponents:

3.) (x3)44.) (m4)2(m3)35.) (g-2)-3(g4)56.) (2w-3)2

7.) (4d2)-38.) (5x2y4)3(2xy2)9.) (p-2)5(p-10)10.) (3.5)3(3.5)-2

11.) (3a2b-4)2(2ab3)312.) (35)2(3-2)413.) (x-2)(3xy2)4

Complete each equation (fill-in-the-blank with a number)

14.) (m4)___ = m1215.) m4∙ m___ = m1216.) (a2b4)___ =

B. Applications to Scientific Notation

  • Raise the coefficient to the given power
  • Multiply the exponents
  • Check to make sure that your answer is in scientific notation

Simplify. Write each answer in scientific notation

17.) (1.2 x 104)2 18.) (2 x 10-9)-2 19.) (-3 x 105)3 20.) (8 x 10-5)2

Combine like terms. Distribute/Multiply first if necessary.

1.) 2.) 3.) 3x(2x – 5) + 4x(8 – 3x)

4.) -7x2(6x – 2) + 3x(8 – 2x2)5.) 5x(3x – 2y) – 2x(3y – 7x)6.) (4x3)2 – (5x4)(6x2)

7.) (3a3)(-4a5) + (2a2)(5a4) + (3a2)4 – (2a3)2

Simplify. Leave your answer in scientific notation.

8.) (5.6 x 104)(6.2 x 107)9.) (3.2 x 106)210.) (4.3 x 108)(12.5 x 104)

11.) (3.2 x 10-5)212.) 4(6.3 x 107)13.) (4.3 x 108)(12.5 x 104)

Notes #4

Section 7.5: Division Properties of Exponents

A. Dividing Monomials

Explore:

1.) 2.)3.)

Dividing Monomials
**When I divide like numbers or variables, I ______their exponents.**

Use this property to simplify the expressions. Leave all answers in positive exponents.

4.) 5.) 6.)

7.)8.)9.)

10.)11.)12.)

B. Fractions to Negative Powers

Explore: This is the same as:

Fractions to Negative Powers
**When I take a fraction to a negative power, I ______the fraction over, and raise it to the ______power. **

13.) 14.)15.) 16.)

C. Applications to Scientific Notation

Dividing Numbers in Scientific Notation
  • Divide Coefficients (decimal terms)
  • Subtract Exponents
  • Check to make sure that the answer is in scientific notation

17.) 18.) 19.)

20.)21.)

Review Topics: Solve for x and y using the method stated below:

22.) Use Substitution:23.) Use Elimination:

Notes #5:Chapter 7 Review

Evaluate:

1.) 2.) -33 3.)(-3)4 4.) -5(6x)0

5.) -4-26.) 7.) (-4a-5b7) (-3a4b-3)28.) (t6)4

9.) 10.) (-2b3c5)(-5b2c)(b2c)11.) (-4w-3)-2(6w5)

Write in standard notation:

12.) -4.602 x 10-513.) 7.041 x 107

Write in scientific notation

14.) 0.00354 15.) 8,900,00016.)(3 x 103)(0.2 x 10-2)

17.) (5.0 x 103)218.)

Simplify:

19.) 20.)

Algebra 1: Chapter 7 Study Guide Name: ______

Per: ______Date: ______

For #1-8, simplify each expression:
1.) (-3)0 / 2.) (4)-2 / 3.) -2-3 / 4.)
5.) (7m4)0 / 6.) (2f)-4 / 7.) 3-2w3x-3y-2 / 8.)
For #9-11, evaluate each expression for m = -2 and n = 3
9.) m-2n / 10.) 2-3m3n-2 / 11.) m-n
For #12-14, write each number in scientific notation:
12.) 0.0065 / 13.) 130,000 / 14.) 0.03025
For #15-17, write each number in standard notation:
15.) 4.3 x 10-3 / 16.) 2.75 x 107 / 17.) 8 x 10-5
For #18-20, is each number written in scientific notation? If not, convert to scientific notation.
18.) 44 x 103 / 19.) 0.5 x 10-4 / 20.) 3.45 x 10-2
For #21-23, rewrite each expression using the base only once
21.) (23)(25)(2-2) / 22.) / 23.) (9.7)-8(9.7)8
For #24-35, simplify each expression. If applicable, leave your answer in scientific notation.
24.) (3bc8)(-5b2c)(2b3c-2) / 25.) (8.5 x 107)(-1.2 x 10-3) / 26.) (d3)2(d2)4
27.) (-5m-2n3)3 / 28.) (2 x 103)2 / 29.) (-3x2y3)2(-8xy5)
30.) / 31.) / 32.)
33.) / 34.) / 35.)
For #36-39, complete each equation (fill in the blank).
36.) / 37.)
38.) / 39.)

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