Key Terms
 Base – A number in exponential form. It appears beneath the exponent.
 Exponent – A small raised number that tells you how many times to multiply the base number by itself.
 Exponential Expression – An expression that involves an exponent.
 The expression may contain variables, which may be the base or the exponent.
 Fractional – Having to do with a fraction.
 The fractional part of the number is
 Power – A small raised number that tells you how many times to multiply the base number by itself. It is also called an exponent.
 Principal Square Root – The positive square root of a number.
 The principal square root of b is written , or .
 If x is the principal square root of n, then .
 Radical – The symbol is used to indicate a square root.
 indicates the nth root.
 is simply written as .
 Scientific Notation – A way to represent very large or very small numbers.
 A number in scientific notation has the form , where N is between 1 and 10 and m is an integer.
Review
Order of Operations



Perfect Squares

Notes
Exponents


Exponent Laws

Examples of Exponent Laws


Powers and Roots


Exponent Rules for Negatives and Zeros


Principal Square Root Rules

Square Roots
Scientific Notation




Examples
Order of Operation Example
 Ex 1. Evaluate:
P:
E:
MD:
AS:
 Answer: 171
Exponent Examples
 Ex 2. Which of the following is equal to the expression below?
 Setup:
 Answer:
 Setup:
 Ex 3. Which of the following is equal to the expression below?
 Setup:
 Simplify:
 Answer:
 Ex 4. Which expression is equal to the expression below?
 The exponent can be distributed
 Answer:
 The exponent can be distributed
 Ex 5. Which of the following is equal to the fraction below?
 Distribute the negative sign
 Answer:
 Distribute the negative sign
 Ex 6. Evaluate:
 Anytime an exponent is raised to the zero power, it equals 1
 Answer:
 Anytime an exponent is raised to the zero power, it equals 1
 Ex 7. What is the equivalent of:
 Add exponents when you are multiplying with the same base
 Answer:
 Add exponents when you are multiplying with the same base
 Ex 8. What is the equivalent of:
 Subtract exponents when you are dividing with the same base
 Answer:
 Subtract exponents when you are dividing with the same base
Square Root Examples
 Ex 9. What is the value of the exponential expression below?
 Any exponential fraction should be translated to a radical. In this case: .
 Setup: , which can be simplified to .
 Answer:
 Ex 10. If z is the principal square root of 8, what must be true?
 Answer: , and z is positive.
 Ex 11. Simplify this radical expression.
 Since only 4 can be squared, you must leave w inside the root.
 Answer:
 Since only 4 can be squared, you must leave w inside the root.
 Ex 12. Simplify this radical expression.
 Since only 36 can be squared, you must leave q inside the root.
 Answer:
 Since only 36 can be squared, you must leave q inside the root.
 Ex 13. Simplify:
 Breakdown into factors, looking for perfect squares:
 Since 4 is a perfect square, take the square root of 4 and leave the 7 inside.
 Answer:
 Ex 14. Simplify:
 Convert the fraction to a square root:
 Break the square root down into individual square roots:
 Since 4 and 9 are both perfect squares, take the square root of each:
 Answer:
 Ex 15. What numbers are square roots of 64?
 Answer: +8 and 8
 Ex 16. What numbers are square roots of 81?
 Answers:
 Ex 17. Which of the following are equal to the expression below?

 Answers:

 Ex 18. Which of the following are equal to the expression below?

 Answer:
