Pre-calculus Review Workshop 1.2 Exponent Rules (no calculators)
Tip. When simplifying radical expressions, it is helpful to rewrite a number using its prime factorization
and cancel powers.
Example. 108 = 2
2
3
3
so
3
p
108 =
3
p
2
2
3
3
=3
3
p
2
2
=3
3
p
4
1. Evaluate each expression.
(a) ( 3)
4
(b) 3
4
(c)
✓
1
8
◆
2
· (2)
3
(d) ( 2)
5
(e) 2
5
(f) ( 6)
2
·
✓
1
6
◆
2
(g)
✓
2
5
◆
0
· 3
1
(h)
3
2
5
0
(i)
✓
2
5
◆
2
(j) 5
2
· 5(k)5
8
· 5
6
(l) 5
8
· 5
6
(m)
2
3
2
(n)
10
8
10
5
(o)
10
2
10
2
2. Simplify.
(a)
p
12 (b)
p
18 (c)
3
p
250
(d)
5
p
243 (e)
5
p
486 (f)
4
p
162
(g)
r
27
16
(h)
p
18
p
36
(i) 5
3
p
81
(j)
p
2 ·
p
6(k)
p
14 ·
p
32 (l)
p
80
p
5
(m)
3
p
500 (n)
4
p
24 ·
4
p
14 (o)
p
63
p
7
(p)
5
r
1
2
·
5
r
1
16
3. Simplify each expression and eliminate negative exponents.
(a) x
5
· x
8
(b) (2x
3
)
2
(c) x
3
· x
5
(d) y
6
· y
9
(e) (3x)
3
(f) y
7
· y
3
(g) z
8
· z
3
(h) x
2
x
6
x
4
(i)
x
15
x
10
(j) y
3
· y
9
(k) w
5
w
8
w
4
(l)
x
8
x
0
x
12
(m)
b
8
b
3
b
(n) (z
3
z
5
)
2
(o) (3x
4
)
⇣
x
3
⌘
3
(p)
y
3
y
5
y
2
y
3
(q) ( 2 b
3
b
3
)
3
(r) ( 3 x
2
)
2
(2x
2
)
3
4. Simplify each expression and eliminate negative exponents.
(a)
xy
7x
4
y
2
(b)
7y
6
4y
5
z
4
(c) (x
3
y
5
)(2x
4
y
2
)(4xy
5
)
(d) (xw)(6x
6
w
4
)(e)(w · 4w
2
· w
2
)
3
(f)
✓
y
2
y
◆
3
(g) (3x · 4x
2
)
3
(h)
✓
2y
4
4y
◆
2
(i)
✓
9z
8z
6
◆
3
(j)
x
3
y
2
y
1
(k)
✓
a
3
b
2
a
3
b
2
◆
3
(l)
✓
x
y
2
◆
5
✓
x
2
y
3
z
2
◆
3
(m)
(a
1
b
3
)
2
(a
2
b
3
)
3
(n)
✓
x
2
z
4
2y
5
◆✓
3x
2
y
3
z
2
◆
2
(o)
(w
2
v)
3
(w
2
v
3
)
2
(p)
16x
3
y
5
4x
6
y
8
(q)
⇣
w
3x
3
⌘
2
(r)
✓
2x
1
y
x
3
y
2
◆
3
5. Express the following in the form x
r
.
(a) (
5
p
x)
6
(b)
8
p
x
3
(c)
1
(
p
x)
5
(d)
1
3
p
x
4
(e)
4
q
3
p
x (f)
s
1
5
p
x
6. Express the following in the form x
r
.
(a) x
5
2
x
3
(b)
x
6
7
x
4
(c) (x
3
)
4
5
(d) x
7
5
x
8
3
(e) (x
2
3
)
4
9
(f)
1
x
5
2
(g)
✓
1
x
3
◆
2
3
(h)
1
x
p
x
(i) x
2
(
3
p
x)(j)
x
x
2
5
(k)
x
1
3
x
(l)
1
x
5
4
7. Simplify and eliminate negative exponents. Assume that all letters denote positive numbers.
(a) x
2
3
· x
4
3
(b) a
3
5
· a
12
5
(c) (9x)
1
2
· (4x
1
4
)
(d) ((2b)
2
9
)
3
· (2b)
1
3
(e)
x
3
2
x
1
2
x
5
2
(f) (27z
3
)
2
3
(g) (x
5
y
4
)
1
2
(h) ( 8 x
6
y
18
)
1
3
y
1
(yx
1
2
)
2
3
(i)
a
3
2
b
1
2
!
4
✓
a
2
b
3
◆
(j)
✓
x
6
y
3
27y
3
5
◆
1
3
Answers
1. (a) 81 (b) 81 (c) 1/ 8(d)32 (e) 32 (f) 1 (g) 1/3(h)1/9
(i) 25/ 4(j)125(k)25(l)1/25 (m) 64 (n) 1000 (o) 10,000
2. (a) 2
p
3(b)3
p
2(c)5
3
p
2(d)3(e)3
5
p
2(f)3
4
p
2(g)
3
p
3
4
(h)
p
2
2
(i) 15
3
p
3(j)2
p
3(k)8
p
7(l)4(m)5
3
p
4(n)2
4
p
21 (o) 3 (p)
1
2
3. (a) x
13
(b) 4x
6
(c) x
2
(d) y
15
(e) 27x
3
(f) y
4
(g)
1
z
5
(h)
1
x
4
(i) x
5
(j)
1
y
6
(k) w (l)
1
x
4
(m) b
4
(n) z
16
(o)
x
7
9
(p) y
9
(q) 8 b
18
(r)
72
x
2
4. (a)
x
5
y
3
7
(b)
7y
4z
4
(c) 8y
2
(d)
6
x
5
w
3
(e) 64w
15
(f) y
3
(g) 1728x
9
(h)
y
6
4
(i)
729
512z
15
(j)
1
x
3
y
(k)
a
18
b
12
(l)
x
11
yz
6
(m)
b
15
a
8
(n)
9x
6
y
2
(o) w
2
v
9
(p)
4x
9
y
13
(q)
9
w
2
x
6
(r)
1
8x
6
y
9
5. (a) x
6
5
(b) x
3
8
(c) x
5
2
(d) x
4
3
(e) x
1
12
(f) x
1
10
6. (a) x
11
2
(b) x
22
7
(c) x
12
5
(d) x
19
15
(e) x
8
27
(f) x
5
2
(g) x
2
(h) x
3
2
(i) x
7
3
(j) x
3
5
(k) x
2
3
(l) x
5
4
7. (a) x
2
(b) a
3
(c) 12x
3
4
(d) 2b (e)
1
x
1
2
(f)
1
9z
2
(g)
1
x
5
2
y
2
(h)
y
6
2x
2
(i)
x
1
3
y
1
3
(j)
a
4
b
(k)
3y
6
5
x
2
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Keystone Algebra 1
ID: 1
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Period____Date________________
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Simplifying Absolute Value Problems
Evaluate each expression.
1)
−1 − 2 2)
9÷
(
3
)
3)
1 − 4 × −2
4)
−
12
−1 + 1
5)
1 −
−3 + 5 6)
(
3 − 3 −
−4
)
× 5
Evaluate each using the values given.
7)
b −
a ; use
a = 5, and
b = 6 8)
x +
y ; use
x = 3, and
y = −5
9)
q −
r ; use
q = 3, and
r = −1 10)
j −
h ; use
h = 5, and
j = 6
-1-
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Worksheet by Kuta Software LLC
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x −
(
z +
x
)
; use
x = 6, and
z = 3 12)
6
x +
y ; use
x = 1, and
y = 1
13)
(
p +
q
)
÷5; use
p = −2, and
q = −3 14)
j
(
h −
h
)
; use
h = −1, and
j = 5
15)
2 +
h +
j ; use
h = 6, and
j = −4 16)
x −
y +
y − 1; use
x = −3, and
y = −6
17)
3 −
(
p +
m −
m
)
; use
m = 4, and
p = −4 18)
n
(
m + −1
)
−
n; use
m = 1, and
n = −6
19)
ab −
b +
b; use
a = 3, and
b = 6 20)
x −
(
x +
y −
−
x
)
; use
x = −2, and
y = 4
-2-
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Keystone Algebra 1
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Simplifying Absolute Value Problems
Evaluate each expression.
1)
−1 − 2
3
2)
9÷
(
3
)
3
3)
1 − 4 × −2
−6
4)
−
12
−1 + 1
−6
5)
1 −
−3 + 5
9
6)
(
3 − 3 −
−4
)
× 5
20
Evaluate each using the values given.
7)
b −
a ; use
a = 5, and
b = 6
1
8)
x +
y ; use
x = 3, and
y = −5
2
9)
q −
r ; use
q = 3, and
r = −1
2
10)
j −
h ; use
h = 5, and
j = 6
1
-1-
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11)
x −
(
z +
x
)
; use
x = 6, and
z = 3
−3
12)
6
x +
y ; use
x = 1, and
y = 1
12
13)
(
p +
q
)
÷5; use
p = −2, and
q = −3
1
14)
j
(
h −
h
)
; use
h = −1, and
j = 5
−10
15)
2 +
h +
j ; use
h = 6, and
j = −4
12
16)
x −
y +
y − 1; use
x = −3, and
y = −6
−4
17)
3 −
(
p +
m −
m
)
; use
m = 4, and
p = −4
7
18)
n
(
m + −1
)
−
n; use
m = 1, and
n = −6
−6
19)
ab −
b +
b; use
a = 3, and
b = 6
18
20)
x −
(
x +
y −
−
x
)
; use
x = −2, and
y = 4
−2
-2-
