Foundations of Math 2 Final Exam Review Name: ______
UNIT 3: EXPONENTS, RADICALS, AND EXPONENTIAL EQUATIONS
Part 1: Exponent Rules
Mathematical Expressions can be simplified used exponent rules
Here are all of the rules:
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ADDING AND SUBTRACTING EXPRESSIONS
When you are adding and subtracting exponents, you must:
______only!
Make sure to ______the ______ when subtracting
Example:
(4x2 + 9x – 6) + (7x2 – 2x – 1) = ______
(3x2 + 5x – 8) – (5x2 – 4x + 6) = ______
MULTIPLYING EXPRESSIONS
When you are multiplying expressions:
______ the whole numbers
______ the exponents
Example:
(4x3)(2x2) = ______
(-4x5)(3x2) = ______
RAISING A POWER TO A POWER
When you are raising a power to a power:
______ the whole numbers to the power
______ the exponents
Example: (5x2)4 = ______
(-3x6)3 = ______
DIVIDING EXPRESSIONS
When you are dividing expressions:
______the whole numbers
______ the exponents
Example:
= ______
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NEGATIVE EXPONENTS
When you have a negative exponent:
______the negative exponent “______”, meaning move it to the other side of the ______
When you move it, change the exponent to a ______because now it’s ______
Example:
= ______
= ______
ZERO EXPONENTS
When you have a zero exponent:
The answer is always ______
Example: = ______
= ______
Practice All Exponent Rules:
1. (5x2 – 5x + 2) + (6x2 + 2x – 10) =
2. (3x2 + 6x – 4) – (6x2 – 2x + 9) =
3. (6x4)(5x2) =
4. (4x2)3 =
5. =
6. =
7. (3x2y)0 =
Part 2: Converting a Radical into a Fractional Exponent
Parts of a radical
When converting a radical to a fractional exponents
The power inside the radical becomes the ______
The number in the ______becomes the ______
Example: = ______
Now try these:
1. = ______3. = ______
2. = ______4. = ______
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Part 3: Converting a Fractional Exponent into a Radical
When converting a fractional exponent to a radical:
The numerator becomes the power ______the radical
The denominator becomes the number in the ______
Example: = ______
Now try these:
1. = ______3. = ______
2. = ______4. = ______
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Part 4: Solving Rational Equations
When solving rational equations with ______terms, you must ______
Example:
5(2x+1) = 20x
10x + 5 = 20x
5 = 10x
x =
You try:
Example: Answer: ______
Part 5: Exponential Growth and Decay
Exponential Functions can either represent ______or ______
Every function follows this formula:
y = a bx
a is the ______ value
b is the ______or ______ rate
If the problem is growth, use (______) for b
If the problem is decay, use (______) for b
x is the ______
Example: Write the equation for this situation: The amount of movies made in 2015 was 1,255. The number is expected to increase by 2.1% every year. ______
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.
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- The number of people who live in North Dakota (who currently has 739,482 people) decreases every year by 1.3%.
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Part 5: 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.
Try this one:
The model y = 604000(1 + 0.045)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? ______
Unit 3: Page 1 of 4