1. Powers and Exponents

2. Vocabulary
POWER– A power is the result of a repeated multiplication of the same factor.
3 x 3 = 3² or 9
3 x 3 x 3 x 3 x 3 = 3 5
or 243

3. Vocabulary
BASE—A base is the number or variable that is used as a factor in repeated multiplication. 3²
The base.

4. Vocabulary
EXPONENT—An exponent is the number that represents the number of times the base is used as a factor.
3 ² _
The exponent

5. Write the product using an exponent.
EXAMPLE 1—Using Exponents
Write the product using an exponent.
7·7·7·7·7= 7
2·2·2 = 2

6. Write the product using an exponent.
EXAMPLE 1—Using Exponents
Write the product using an exponent.
(0.4)(0.4)= (0.4)

7. Write the product using an exponent.
EXAMPLE 1—Using Exponents
Write the product using an exponent.
x·x·x·x = x
r·r = r

8. Evaluate the expression x³ when x = 0.4
EXAMPLE 2—Evaluating Powers with Variables
Evaluate the expression x³ when x = 0.4

9. AREA AND VOLUME FORMULAS
Area is measured in square units ( ft² ). Volume is measure in cubic units ( ft³ ).

10. Remember, you cannot add or subtract variables with different exponents. They are not "like variables."
However, you CAN multiply and divide them!

11. Product Rule
-When multiplying like variables with exponents, write the base and ADD the exponents. +
x² * x³ = x 5
ex.
x³ * x 4 =

12. Quotient Rule
-When dividing like variables with exponents, write the bases and subtract the exponents. - x² x 6
___ = x 4 x
___ 5 8 =
ex.

13. Solve. Then write the rule you are using.3 2
___ =
y * y 6 5 =
t * t 5 3 = x __ 9 =

14. HW:
Exponents: Product Rule and Quotient Rule worksheet

15. r t * t * t y * y t * t x² * x x _____ x __ 4 5 5 23 ___ = 12 = 5 2 =9 x 4
_____ = x __ 9 = 4

16. Product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property