1. Exponents
An exponent is the number of times the base is multiplied by itself.
Example
27 can also be written as 3
This means 3 X 3 X 3 3

2. Substituting variables for numbers
We can also use variables such as X and Y when using exponents. We can define X and Y as integers.
For example:
3 = 3 X 3 X 3 = 27 SO: X = (X)(X)(X) 3 3

3. Variable
A variable is a symbol for a number we don’t know yet like X or Y.

4. Integers
Integers include zero, positive and negative numbers. They do not include fractions.

5. Laws of Exponents N
X = (X)(X)…..(X) (N factors of X) X = 1 (if X = 0) X X = X -n n
1/N N

6. Practice Write 11 as multiplication.3
Write 11 as multiplication.
Write u as a fraction using only positive exponents.
What is the value of ?
Evaluate and (-5) -7
1/2 -2 -2

7. Solutions
11 X 11 X 11 = 1331 1 u 10 25 7

8. Multiplying Exponents
Same base
(X ) (X) = X
Be careful I can add the exponents, because X is the base both time. If I had X and Y I could only combine in the exponents were the same. 5 6 11

9. Differences Math is a language3 3 3
(4x) means (4 ) (X )
4x means 4 (X)(X)(X) 3

10. Dividing Exponents Step 1: X X = Step 2: X = 1 X Step 3: (X ) (X ) = X8 6
Step 1: X X = Step 2: X = 1 X Step 3: (X ) (X ) = X 8 6 2 8 -6

11. Dividing Exponents 8 6
Step 1: X X = Step 2: (XX) (XXXXXX) (XXXXXX) STEP 3: (XX) (XXXXXX) (XXXXXX) Step 3: (XX) = X 2

12. x Anything divided by itself is 1. X to the zero power is 1.
Anything divided by itself is 1. X to the zero power is 1.
Example X / X = (X ) (X ) = 1
This works in all cases except for if X is equal to zero. 3 -3 3 3