Date: 9/4 or 9/5 Exponents – Multiplication and Division Properties Definition: Base Definition: Exponent Example 1: 23×25 Example 2: 710×750 Summary: Definition: In ax, the base is a. (base)2 “It’s the number we are working with” BASE Example: 23 The base = 2 Non-­‐example: 23 The base is not 3 Definition: 2EXPONENT In ax, the exponent “How many times we multiply the base by is x. itself” EXPONENT Example: Non-­‐example: 3 3 2
2
The exponent is not 2 The exponent = 3 Method 1: Method 2: Method 1: Method 2: Example 3: 510×5-­‐5 Example 4: 2!
2!"
Example 5: 10!""
10!"
PEMDAS Hint Method 1: Method 2: Method 1: Method 2: When we multiply powers, we add the exponent. For example, in 210×25 we add 10+5 and get that 210×25 = 210+5 = 215. Similarly, when we divide powers, we subtract. For example, in 210/25 we subtract 10-­‐5 and get that 210/25 = 210-­‐5 = 25. Summary: For multiplication, axay = ax+y. For division, ax/ay = ax-­‐y. Note, you always need the same base and only play with the exponent when doing these operations, not both the exponent and base.