1. Rules of Exponents

2. Exponential Expression
An exponential expression is:
where is called the base and is called the exponent
An exponent applies only to what it is immediately adjacent to (what it touches)
Example:

3. Meaning of Exponent
The meaning of an exponent depends on the type of number it is
An exponent that is a natural number (1, 2, 3,…) tells how many times to multiply the base by itself
Examples:

4. Rules of Exponents
Product Rule: If you have the same base, you can add the exponents.
If bases are different, you can’t add them.
Examples:

5. Let’s prove it! 34 x 32 = (3 x 3 x 3 x 3) x (3 x 3) = (81) x (9) = 729

6. Rules of Exponents
Power of a Power Rule: When an exponential expression is raised to a power, you can multiply the exponents.
Examples:

7. Prove it! (34)2 = (3 x 3 x 3 x 3)2 = (81)2 = (81 x 81) = 6561
38 = 6561

8. Quotient Rule for Exponential Expressions
When exponential expressions with the same base are divided, the result is an exponential expression with the same base and an exponent equal to the numerator exponent minus the denominator exponent
Examples: .

9. Rules of Exponents
Power of a Product Rule: When a product is raised to a power, you can raise each number to that power
Examples:

10. Rules of Exponents
Power of a Quotient Rule: When a quotient is raised to a power, the result is the quotient of the numerator to the power and the denominator to the power
Example:

11. Don’t Make Up Your Own Rules!
Remember PEMDAS
Proof:

12. Any number to the 0 power is 1
Powers of ZERO???
Any number to the 0 power is 1
Why?

13. The Zero Power
What is the pattern?
Divide by 2 each time. So…

14. Review of Math Vocabulary
You may review these on your own.
The power point is on Mrs. Laabs’s Website.

15. Review of Terminology of Algebra
Constant – A specific number
Examples of constants:
Variable – A letter or other symbol used to represent a number whose value varies or is unknown
Examples of variables:

16. Review of Terminology of Algebra
Expression – constants and/or variables combined with one or more math operation symbols for addition, subtraction, multiplication, division, exponents and roots in a meaningful way
Examples of expressions:
Only the first of these expressions can be simplified, because we don’t know the numbers represented by the variables

17. Review of Terminology of Algebra
Term – an expression that involves only a single constant, a single variable.
Examples of terms:

18. Review of Terminology of Algebra
Every term has a “coefficient”
Coefficient – the constant factor of a term
(If no constant is seen, it is assumed to be 1)
What is the coefficient of each of the following terms?

19. Review of Like Terms
Recall that a term is a constant, a variable, or a product of a constant and variables
Like Terms: have exactly the same variables with exactly the same exponents, but may have different coefficients
Example of Like Terms:

20. Review of Like Terms Given the term:
Which of the following are like terms to this one?

21. Adding and Subtracting Like Terms
When “like terms” are added or subtracted, the result is a like term and its coefficient is the sum or difference of the coefficients of the other terms
Example: