Question

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 answer:
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

Answer 1

1

Explanation:

1111111

Answer 2

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