Exponents
Practice
1 Exponents Tutorial
1.1
Notation
Write in either exponent form or as a repeated multiplication
1) 2 × 2 × 2
Note:
When you have a repeated multiplication, you
2) 5 × 5 × 5 × 5 × 5 × 5 × 5
put the number of times you multiply as the
3) 64
exponent. For example: 3 × 3 × 3 × 3 = 34
2
4) 10
1.2
Multiplication Law
5) x3 × x2
6) g−1 × g−5 × g × g5
7) t2 × t6
8) c2 × c2 × c2
9) a3 × b2
10) h × k2
11) (m−4)(n12)(m10)
12) a3 × b9 × c4
1.3
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
Note:
When we are multiplying two numbers with the
same base, you can add the exponents. For
example: a3 × a2 = a3+2 = a5
Note:
When we are multiplying two numbers that DO
NOT have the same base, we CANNOT add the
bases.
Division Law
x10
Note:
x9
a2
a10
4
z ÷ z2
If two exponential numbers are being divide and
they have the same, we subtract the exponent in
the numerator by the exponent in the
denominator. For example: xx = x8−5 = x3
8
c3
c5
5
e−1
e2
b−3
b−5
9
t ÷ t5
a3 ÷ b 2
h4
k9
4
d ÷ e5
j5 ÷
k4
g2
Version 1.4
Note:
When we are dividing two numbers that DO
NOT have the same base, we CANNOT subtract
the bases.
The Math Centre
Liberal Arts and Science
North Campus: GH203, Lakeshore: F201 & www.humber.ca/liberalarts/math-centre
1
Exponents
Practice
1.4
24)
25)
26)
27)
28)
29)
30)
Power Law
(a2 )3
Note:
When we are taking the power of a base that
already has an exponent, we multiply the two
exponents. For example: (a4)2 = a4×2 = a8
(v 3 )3
(62 )4
2(m5 )4
(p2 q)3
Note:
When we have two terms that are both being
brought the power of some number, then we must
being both term to that power. For example:
(de)7
( y1 )19
(3a4 )2 = 32 × (a4 )2 = 9a8
1.5
31)
32)
33)
34)
35)
36)
Inverse Law
a−3
Note:
When the exponent is a negative we place the
base and the exponent at the bottom of a
fraction. For example: a−1 = a1
−(k −1 )−1
(g −2 )−4
k −3
1
h−2
3 −5 4
( xa3 yb−5cz4 )−1
2 Using all the Laws
6m x −2
37) ( 3m
)
n
38) (−5x−5)(2xy7)(−y3)2
39) 9y−xz × −12y
−x
× 15a
40) 12a
5b
b
41) ( ac b )( bac )( ab c )
(3yz)
)
42) (2x
× (4x
9y z
)
43) ( −p7 q )( −9p14 q )
44) (−3m2 ÷ 7n4) × (2n ÷ m)
45) ( s c t )−2
46) x 6y × x 3 z × y 2
47) ( 3xv yw z )0
48) (x−2y2)−2
3 0
2 3
−3
12
9 3
11
3
2
4 3
2 3
4 3
3
4
2
2 4
2
2 2
4 2
3 8
5
−3
4
3 5
−2 2
−3
12 8 4
15
7
Version 1.4
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Liberal Arts and Science
North Campus: GH203, Lakeshore: F201 & www.humber.ca/liberalarts/math-centre
2
Exponents
Practice
Answers/Solutions
1) 23
2) 57
3) 6 × 6 × 6 × 6
4) 10 × 10
5) x5
6) g0 or 1
7) t8
8) c6
9) a3 × b2
10) hk2
11) (m6)(n12)
12) a3 × b9 × c4
13) x1 or x
14) a−1
15) z2
16) c1 or c−2
17) e1 or e−3
18) b2
19) t4
20) ab
21) hk
22) de
2
3
3
2
4
9
4
5
23)
j 4 ×g 2
k4
Version 1.4
The Math Centre
Liberal Arts and Science
North Campus: GH203, Lakeshore: F201 & www.humber.ca/liberalarts/math-centre
3
Exponents
Practice
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
a6
v9
68
2m2 0
p6 q 3
d7 e7
1
y 19
1
a3
−k
g8
1
k3
h2
a−3 b5 c−4
x−3 y 5 z −4
or xa yb zc
3 5 4
3 5 4
n6
4m2
−10y 13
x4
−4x
3y 12 z 3
36a4
b3
a4 b 3 c 3
1
9q 7
2p2
−6m
7n3
s 6 c8
t2
xy 2 z 2
36
1
x4
y4
Version 1.4
The Math Centre
Liberal Arts and Science
North Campus: GH203, Lakeshore: F201 & www.humber.ca/liberalarts/math-centre
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