1. Exponents and Scientific Notation
Chapter 7
Exponents and Scientific Notation

2. 7-1
Zero and Negative Exponents

3. Vocabulary
Power-The base and the exponent of an expression of the form aᴺ
Exponent-A number that shows repeated multiplication.
Base-A number that multiplied repeatedly

4. Vocabulary continued
Simplify-To replace an expression with its simplest name of form.
Evaluate-To substitute a given number for each variable, and the simplify.
Scientific Notation-A number expressed in the form a x 10ᴺ, where n is an integer and 1<|a|<10.

5. 5² What is an Exponent Power How to Say it
What is the power? What is the base? What is the exponent?
Power
How to Say it
10²
Ten squared or ten to the second power 9³
Nine cubed or nine to the third power 3⁴
Three to the fourth power 4⁵
Four to the fifth power

6. Evaluate
5² = 5 x 5 = 25
6³ =
7⁴ =
8⁵ =

7. Simplify numeric base with negative exponent
Make a fraction (if not already a fraction) and move the exponent.
- if the exponent is on top of the fraction, move to the bottom.
- if the exponent is on the bottom of the fraction, move to the top.
- exponent will then be positive
Evaluate.
7¯² = 7¯² 1 = 1 7² = ¯³ = 4³ = 64

8. Examples: Simplify Together 1. 1 5¯³ 2. 4¯³ 3. 4b¯³k⁵ On Your Own
a. 8¯² b. 1 2¯⁴ c. 9a¯²x¯⁹

9. Simplify numeric base with zero exponent
Zero as an Exponent: for every nonzero number a, aᴼ = 1 5ᴼ = 1 (-8)ᴼ = 1

10. Move a single variable base with a negative
Negative Powers: parentheses attach the negative sign to the base number.
-3³ = -1 x 3 x 3 x 3 = -27
(-3)³ = -3 x -3 x -3 = -27
(-3)² = -3 x -3 = 9

11. Examples: Evaluate Together -9³ 2. (-7)² 3. 1 −5¯³ On Your Own
-9³ (-7)² −5¯³
On Your Own
a. (-10)¯² b. -6⁴

12. Homework
Page 195
1-26 all