1. Algebra I Chapter 7 Notes
Rules of Exponents

2. Section 7-1
Monomial – Constant – Base – Exponent -

3. Section 7-1
Monomial – a number, a variable, or the product of a number and variable with non-negative, integer exponents Constant – a monomial that is a real number Base – term being multiplied in an exponential expression Exponent – the number of times the base is multiplied in an exponential expression

4. Section 7-1: Multiplication Rules of Exponents, Day 1
Ex) Determine whether each expression is a monomial. Write yes or no, explain WHY. a) 10 b) f + 24 c) d) e) -5y

5. Section 7-1: Multiplication Rules of Exponents, Day 1
Product of Powers Ex) Simplify each expression a) b) c)
Words
To multiply two powers that have the same base, you add their exponents
Symbols
For any real number a, and any integers m and p:
Examples

6. Section 7-1: Multiplication Rules of Exponents, Day 1
Power of a Power Ex) Simplify a) b)
Words
To raise a power to another power, you multiply the exponents
Symbols
For any real number a, and any integers m and p,
Example

7. Section 7-1: Multiplication Rules of Exponents, Day 2
Power of a Product Ex) Simplify each expression a) b) c) d)
Words
Exponents can be distributed when terms are being multiplied
Symbols
For any real numbers a and b, and any integer m,
Examples

8. Section 7-1: Multiplication Rules of Exponents, Day 2
Ex) Use all rules to simplify a) b) c) d)

9. Section 7-2: Division Rules of Exponents, Day 1
Quotient of Powers Ex. Simplify a) b) c)
Words
To divide two powers with the same base, subtract the exponents
Symbols
For any nonzero number a, and any integers m and p,
Examples

10. Section 7-2: Division Rules of Exponents, Day 1
Power of a Quotient Ex) Simplify a) b) c) d)
Words
To find the power of a quotient, find the power of the numerator and the power of the denominator
Symbols
For any real numbers a and b does not = zero,
and any integer m,
Examples

11. Section 7-2: Division Rules of Exponents, Day 1
Simplify using division rules of exponents 1) 2) 3) 4) 5) 6)

12. Section 7-2: Division Rules of Exponents, Day 2
Zero Exponent Property Ex) Simplify. Assume no denominator = zero a) b) c)
Words
Any nonzero number raised to the zero power is equal to 1
Symbols
For any nonzero number a,
Example

13. Section 7-2: Division Rules of Exponents, Day 2
Negative Exponent Property Ex) Simplify. NO NEGATIVE EXPONENTS! a) b) c) d)
Words
For any nonzero number a, and any integer n, is the reciprocal of
Symbols
For any nonzero number a and integer n,
Examples or

14. Section 7-2: Division Rules of Exponents, Day 2
Simplify using division rules of exponents 1) 2) 3) 4)

15. Section 7-4: Scientific Notation
Scientific Notation – a number written in the form , where 1 < a < 10 and n is an integer. Ex) Write the following numbers in scientific notation. 1) 201,000,000 2)

16. Section 7-4: Scientific Notation
Ex) Write the following numbers in standard form 1) 2)

17. Section 7-4: Multiplying with Scientific Notation
Ex) Use rules of exponents to multiply the following numbers together. Express your answer in both scientific notation and standard form! 1) 2)

18. Section 7-4: Dividing with Scientific Notation
Ex) Use rules of exponents to multiply the following numbers together. Express your answer in both scientific notation and standard form! 1) 2)

19. Section 7-5: Exponential Functions – Exponential Growth, Day 1
Exponential Function – A function that can be written in the form , where a cannot be 0, b > 0, and b cannot be 1. Examples of exponential functions: , , or Exponential Growth
Equation
where
Domain and Range
Intercepts
End Behavior

20. Section 7-5: Exponential Functions – Exponential Growth, Day 1
Graph of Exponential Growth

21. Section 7-5: Exponential Functions – Exponential Growth, Day 1
Ex) Graph , Find the y-intercept, and state the domain and range. You will have to create a table to graph! What is the pattern on the table? x y -2 -1 1 2

22. Section 7-5: Exponential Functions – Exponential Decay, Day 2
Equation
where
Domain and Range
Intercepts
End Behavior

23. Section 7-5: Exponential Functions – Exponential Decay, Day 2
Graph of Exponential Decay

24. Section 7-5: Exponential Functions – Exponential Decay, Day 2
Ex) Graph , Find the y-intercept, and state the domain and range. You will have to create a table to graph! What is the pattern on the table? x y -2 -1 1 2

25. Section 7-6: Exponential Growth and Decay Patterns, Day 1
Equation for Exponential Growth:
a: initial amount t : time y: final amount
r: rate of change expressed as a decimal, r > 0
Ex) The prize for a radio station contest begins with a $100 gift card. Once a day, a name is announced. The person has 15 minutes to call or the prize increases 2.5% for the next day.
Write an equation representing the amount of the gift card after t days with no winner
How much will the card be worth if no one claims it after 10 days?

26. Section 7-6: Exponential Growth and Decay Patterns, Day 1
Compound Interest – interest earned or paid on both the initial investment AND previously earned interest. It is an application of exponential growth.
Equation for Compound Interest
A: current amount P: principal/initial amount
r: annual interest rate expressed as a decimal
n: number of times interest is compounded per year
t: time in years

27. Section 7-6: Exponential Growth and Decay Patterns, Day 1
Ex) Maria’s parents invested $14,000 at 6% per year compounded monthly. How much money will there be in the account after 10 years?

28. Section 7-6: Exponential Growth and Decay Patterns, Day 2
Equation for Exponential Decay
a: initial amount y = final amount
t: time r: rate of decay as a decimal 0 < r < 1
Ex) A fully inflated raft is losing 6.6% of its air every day. The raft originally contained 4500 cubic inches of air.
Write an equation representing the loss of air
Estimate the amount of air in the raft after 7 days

29. Section 7-6: Exponential Growth and Decay Patterns, Day 2
Solve the 3 problems. You must choose which equation to use on each.
Paul invested $400 into an account with 5.5% interest compounded monthly. How much will he have in 8 years?
Ms. Acosta received a job as a teacher with a starting salary of $34,000. She will get a 1.5% increase in her salary each year. How much will she earn in 7 years?
In 2000 the 2200 students attended East High School. The enrollment has been declining 2% annually. If this continues, how many students will be enrolled in the year 2015?