1. Unit 3: Exponents, radicals, and exponential equations
Final Exam Review

2. Topics to cover Exponent Rules
Converting Radicals to Fractional Exponents
Converting Fractional Exponents to Radicals
Exponential Growth and Decay
Word Problems

3. Exponent rules
Mathematical Expressions can be simplified used exponent rules
Here are all of the rules:
ADDING AND SUBTRACTING EXPRESSIONS
MULTIPLYING EXPRESSIONS
RAISING A POWER TO A POWER
DIVIDING EXPRESSIONS
NEGATIVE EXPONENTS
ZERO EXPONENTS

4. ADDING AND SUBTRACTING EXPRESSIONS
When you are adding and subtracting exponents, you must:
COMBINE LIKE TERMS only!
Make sure to DISTRIBUTE the NEGATIVE when subtracting
Example:
(4x2 + 9x – 6) + (7x2 – 2x – 1) = x2 + 7x – 7
(3x2 + 5x – 8) – (5x2 – 4x + 6) = x2 + 9x – 14

5. Multiplying expressions
When you are multiplying expressions
MULTIPLY the whole numbers
ADD the exponents
Example:
(4x3)(2x2) = x5
(-4x5)(3x2) = x7

6. Raising a power to a power
When you are raising a power to a power:
RAISE the whole numbers to the power
MULTIPLY the exponents
Example:
(5x2) = x8
(-3x6) = x18

7. Dividing expressions When you are dividing expressions:
DIVIDE the whole numbers
SUBTRACT the exponents
Example:
6𝑥 4 4𝑥 = 𝟑𝒙 𝟐 𝟐
8𝑥 3 𝑦 𝑥 8 𝑦 = 𝟒𝒚 𝟒 𝟓 𝒙 𝟓

8. Negative exponents When you have a negative exponent
MOVE the negative exponent “TO THE OTHER BUNK”, meaning, move it to the other side of the FRACTION
When you move it, change the exponent to a POSITIVE because now it’s “HAPPY”
Example:
𝑥 −5 𝑦 − = 𝒚 𝟐 𝒙 𝟓
𝑥 2 𝑦 −7 𝑥 −5 𝑦 = 𝒙 𝟐 𝒙 𝟓 𝒚 𝟒 𝒚 𝟕 = 𝒙 𝟕 𝒚 𝟏𝟏

9. Zero exponents When you have a zero exponent The answer is always ZERO
Example:
(5x4y2) =
4𝑥 3 𝑦 2 6𝑥 −4 𝑦− =

10. Practice all exponent rules
(5x2 – 5x + 2) + (6x2 + 2x – 10)
(3x2 + 6x – 4) – (6x2 – 2x + 9)
(6x4)(5x2)
(4x2)3
𝟖𝐱 𝟓 𝐲 𝟐 𝟏𝟐𝐱 𝟑 𝐲 𝟗
𝟔𝐱 𝟓 𝐲 −𝟓 𝟖𝐱 −𝟐 𝐲 𝟑
(3x2y)0

11. Converting a radical into a fractional exponent
Parts of a radical
When converting a radical to a fractional exponent:
The power inside the radical becomes the NUMERATOR
The number in the INDEX becomes the DENOMINATOR
Example: 𝑥 3 = 𝑥 3 5

12. Converting a radical into a fractional exponent
Now try these:
7 𝑥 6
𝑥 3
6 (2𝑥) 11
3 2𝑥 4

13. Converting a fractional exponent into a radical
When converting a fractional exponent into a radical:
The numerator becomes the power INSIDE the radical
The denominator becomes the number in the INDEX
Example: 𝑥 = 𝑥 2

14. Converting a fractional exponent into a radical
Now try these:
𝑥 4 5
3𝑥 1 2
(6𝑥) 6 11
𝑥 5 4

15. Exponential growth and decay
Exponential Functions can either represent GROWTH or DECAY
Every function follows this formula:
y = a bx
a is the INITIAL value
b is the GROWTH or DECAY rate
If the problem is growth, use (1 + rate) for b
If the problem is decay, use (1 – rate) for b
x is the TIME

16. Exponential growth and decay
Example
Write the equation for this situation:
The amount of movies made in 2015 was 1, The number is expected to increase by 2.1% every year.
Answer: y = 1255( )x

17. Exponential growth and decay
Now try these
Write an equation for these situations:
The population of an ant colony with 5,056 members increases by 5.6% every year.
The number of people who live in North Dakota (who currently has 739,482 people) decreases every year by 1.3%.

18. Word problems
There are many real life situations that use exponential growth and decay. You can use these equations in order to predict outcomes in the future.
In order to do this, use your calculator to put in the equation and use the table to find values.

19. Word problems Try this one:
The model y = ( )x represent the population of Washington DC after 1990.
1. Find the initial population
2. Is this a growth or decay problem?
3. Predict the population in 1995.
4. In what year will the population reach 1,000,000?

20. ALL DONE