Write each number using exponents. 1) 6 x 6 = 2) -5 x -5 x -5 x -5 =
3) 27 = 4) - (4 x 4 x 4) =
5) a x a x a = 6) 1
2
x
1
2
x
1
2
x
1
2
x
1
2
x
1
2
=
7) -122 base Expanded 8) (
1
2
)
3 base Expanded
Exponent Standard form Exponent Standard form

9) (-9)3
base Expanded
Exponent Standard form
Write in expanded form.
10) 84 11) -3
2

12) 8 squared 13) (-7)5
14) 7 cubed 15) (
3
4
)
5

Write in standard form.
16) 81 = 17) -2
4
=
18) 4 squared = 19) (-2)4 =
20) 5 cubed = 21) (-3)3 =
22) (
3
5
)
2 = 23) -3
3
=
Write each expression in standard form. Then compare using <, >, or =.
24) 32
23
25) 73
7 x 7 x 7
26) 53
5 x 3 27) (-3)2 -2
4
28) 2 squared 2 cubed 29) 43
4 cubed
Circle the correct
30) 48 in exponential notation: 86 6
8 480 481

31) Base is 4, Exponent is 5: 45 4 x 5 45
5
4
32) 216 in exponential notation: 63 3
6 2160 216
33) 23 + 34 5
7 2334 89 18
Investigating Exponent Properties: Product of Powers
Expression Expand the expression Simplified
Expression

5
2
∙ 5
4 ∙ ∙ 5 ∙ 5 ∙ 5 ∙ 5 5
6
8
4
∙ 8
5
(−4)
3
∙ (−4)
5
7
4
∙ 7
4
∙ 7

3
∙
7
5
4
2
∙ 3
6
9 Try this one without expanding it.
Do you see a pattern that relates the expression in the first column to the
equivalent simplified expression? Write in words what you notice about the
exponents.
Try these on your own
7
15
9
2 ∙ 8
0
5
Here is the formal rule when multiplying exponential expressions with
the same base:
Investigating Exponent Properties: Quotient of Powers
Expression Expanded form Cancel factors Simplified
Expression

4
3
4
2
4 ∙ 4 ∙ 4
4 ∙ 4
4∙4∙
4∙4
4
1
3
6
3
3
1
5
1
4

9

7
6
15
45
6
725
Try this one without expanding it.
Do you see a pattern that relates the expression in the first column to the
equivalent simplified expression? Write in words what you notice about the
exponents.
Try these on your own
Here is the formal rule when dividing exponential expressions with the
same base:
9
7

8
6
5
8
33
Investigating Exponent Properties: Power of a Power
Expression Expanded Form Expand further Simplified
Expression

(9
2
)
3 9
2
∙ 9
2
∙ 9
2 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9 9
6
(8
3
)
4
[(−6)
2
]
5
(
3
)
3
(
4
∙
2
)
3
(
20)
32 Try this one without expanding it.
Do you see a pattern that relates the expression in the first column to the
equivalent simplified expression? Write in words what you notice about the
exponents.
Try these on your own
4
24
(
2
5

3
)
3
Here is the formal rule when multiplying exponential expressions by a
power