h

1. Powers and Exponents

2. Vocabulary
POWER– A power is another name for an exponent. It
is the result of a repeated multiplication of the same
factor.
1 x 3 x 3 = 3² or 9
1 x 3 x 3 x 3 x 3 x 3 = 3
5
or 243
9

3. Vocabulary
BASE—the number or variable that is used as a factor
in repeated multiplication.
3²
The base.
or x²

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
or
x²

5. Write the product using an exponent.
7·7·7·7·7= 7
2·2·2 = 2
1
2
(0.4)(0.4)= (0.4)
3

6. Write the product using an exponent.
x·x·x·x = x
r·r = r
4
5

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

8. Exponent Rules

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

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

11. y * y
6
5 =
r
3
2
r
___ =
t * t
5 3
=
x
x
__
9
=
Solve. Then write the rule you are using.
6
7
8
9

12. Power to a Power Rule
-When raising an exponent to a new power, multiply the
two exponents.
(x²)³ = x
6
*
ex. (x²)
7
=

13. Product to a Power Rule
When a product is raised to a power, raise the
WHOLE THING to the exponent.
(xy)³ = x³y³
ex. (3abc)² =

14. Quotient to a Power Rule
When a quotient is raised to a power, raise the
WHOLE THING to the exponent.
x²
__
y
4 )
) 3
=
x
__
y
12
6
*
*
ex.
r³
___
p²
)
) ²
=

15. Zero Power Rule
Any number or variable to the zero
power is equal to 1.
x = 1
0
0
3 =
ex.

16. 2xy
3x
( (
0
=
x² )
) ³
=
3² )
) ³
=
(ab)
5
=
4
0
=
(3x)²
___
x
=
x
__
x
=
(x²y³)
4
=
WRITE THESE DOWN!
(mp)
____
p
4
=
4
10
12
13
14
15
11
16
17
18

17. HW: Exponent Rules Practice worksheet