Exponent Laws WS Name_____________Block:_______Date:___________
#1

Remember: When you are working with powers with the same base, you can simplify the
question using some basic math ideas.
Example 1:
52 x 54
Expanded
(5 x 5) (5 x 5 x 5 x 5)
Same as
5x5x5x5x5x5
notice they are all 5s?!
Which is
56
Try these:
(-3)7 x (-3)3
63 x 65 x 6
=
=
Example 2:
89 ÷ 83
888888888
888
Expanded:
8
1
8
86
Which is the same as
Example 3:
Note:
888888
Remove all the 1s to get:
Try these:
89
83
which is the same as
1110 ÷ 117
42 x 33
(-2)8 ÷ (-2)7
if the bases are DIFFERENT this is just a
BEDMAS question
Expand
4x4x3x3x3
Multiply
16 x 27 = 432
 Practice:
1. Write each expression as a single power. Then, evaluate.
Single Power
4+5
Evaluate (find the answer)
a) 24 × 25
2
b) (–4)2 × (–4)2
______
______
c) 62 × 6
______
______
d) 93 × 92
______
______
=2
______
2. Write each expression as a product of two powers, then as a single power.
Product of Two
Powers
Single Power
a) (3 × 3 × 3 × 3)(3 × 3)
3
3
b) (5 × 5 × 5 × 5)(5 × 5 × 5 × 5 × 5 × 5)
____________
______
c) (8 × 8 × 8 × 8 × 8 × 8)(8 × 8 × 8 × 8 × 8)
____________
______
d) (11 × 11 × 11)(11 × 11)
____________
______
x 3
+
=3
3. Write each expression as a single power. Then, evaluate.
Single Power
Evaluate
a) 34 ÷ 32
______
______
b) (–5)3 × (–5)2
______
______
c) 29 x 2
______
______
d) 82 ÷ 82
______
______
The multiplication law of exponents says: if you are multiplying powers with
the same base _____________________________________________
4. Write each expression as a quotient of two powers, then as a single power.
Math9a
Ms. Burton & Mrs. Wong
Quotient of
Two Powers
÷ 5
Single
Power
5
= 5
a) (5 × 5 × 5 × 5) ÷ (5 × 5)
5
b) (7 × 7 × 7) ÷ (7 × 7 × 7)
____________
______
c)
8888888
8888
____________
______
d)
(2  2  2  2  2  2)
(2  2  2  2  2)
____________
______

The division law of exponents says: if you are dividing powers with the same
base _____________________________________________
5. Simplify the following using the exponent laws if possible then evaluate:
a) 42 x 45 x 4
____________
______
b) 63 x 64 ÷ 62
____________
______
c) 102 x 23
____________
______
d) (-7)8 ÷ (-7)5
____________
______
e) (-3)10 ÷ (-3)5 x (-3)2
____________
______
f) 42 + 42
____________
______
Answers (scrambled):
29
510
210
21
(-7)3
Math9a
216
7776
65536
256
(-4)4
36
63
811
95
115
32
-5
(-3)7
52
(-5)1
32
80
83
48
65
800
512
59049
9
1024
1
70
-343
-2187
Ms. Burton & Mrs. Wong