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Math Problems
Algebra 2
Simplify rational expressions
Select all the expressions that are equivalent to
1
2
2
6
2
\frac{12^2}{6^2}
6
2
1
2
2
.
\newline
Multi-select Choices:
\newline
(A)
2
−
3
2
−
5
\frac{2^{-3}}{2^{-5}}
2
−
5
2
−
3
\newline
(B)
2
2
2
\newline
(C)
(
2
−
2
)
−
1
(2^{-2})^{-1}
(
2
−
2
)
−
1
\newline
(D)
2
2
2^2
2
2
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Select all the expressions that are equivalent to
2
6
×
2
9
2^6 \times 2^9
2
6
×
2
9
.
\newline
Multi-select Choices:
\newline
(A)
(
2
5
)
3
(2^5)^3
(
2
5
)
3
\newline
(B)
1
2
15
6
15
\frac{12^{15}}{6^{15}}
6
15
1
2
15
\newline
(C)
2
54
2^{54}
2
54
\newline
(D)
2
15
2^{15}
2
15
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Select all the expressions that are equivalent to
6
6
2
6
\frac{6^6}{2^6}
2
6
6
6
.
\newline
Multi-select Choices:
\newline
(A)
3
3
3
\newline
(B)
1
3
6
\frac{1}{3^6}
3
6
1
\newline
(C)
3
0
3^0
3
0
\newline
(D)
3
6
3^6
3
6
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Select all the expressions that are equivalent to
3
2
3
2
\frac{3^2}{3^2}
3
2
3
2
.
\newline
Multi-select Choices:
\newline
(A)
1
1
1
\newline
(B)
1
3
0
\frac{1}{3^0}
3
0
1
\newline
(C)
3
0
3^0
3
0
\newline
(D)
3
4
3^4
3
4
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Select all the expressions that are equivalent to
(
6
1
)
5
(6^1)^5
(
6
1
)
5
.
\newline
Multi-select Choices:
\newline
(A)
6
5
6^5
6
5
\newline
(B)
1
6
−
5
\frac{1}{6^{-5}}
6
−
5
1
\newline
(C)
1
6
6
\frac{1}{6^6}
6
6
1
\newline
(D)
1
6
5
\frac{1}{6^5}
6
5
1
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Select all the expressions that are equivalent to
8
−
2
×
7
−
2
8^{-2} \times 7^{-2}
8
−
2
×
7
−
2
.
\newline
Multi-select Choices:
\newline
(A)
1
5
6
2
\frac{1}{56^2}
5
6
2
1
\newline
(B)
5
6
4
56^4
5
6
4
\newline
(C)
5
6
−
2
56^{-2}
5
6
−
2
\newline
(D)
5
6
−
4
56^{-4}
5
6
−
4
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Select all the expressions that are equivalent to
(
7
5
)
1
(7^5)^1
(
7
5
)
1
.
\newline
Multi-select Choices:
\newline
(A)
1
7
5
\frac{1}{7^5}
7
5
1
\newline
(B)
1
7
−
5
\frac{1}{7^{-5}}
7
−
5
1
\newline
(C)
7
5
7^5
7
5
\newline
(D)
7
6
7^6
7
6
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Simplify the rational expression:
\newline
2
q
2
−
q
r
−
3
r
2
2
q
2
−
9
q
r
+
9
r
2
\frac{2q^{2}-qr-3r^{2}}{2q^{2}-9qr+9r^{2}}
2
q
2
−
9
q
r
+
9
r
2
2
q
2
−
q
r
−
3
r
2
\newline
A)
(
q
+
r
)
/
(
k
+
3
r
)
(q+r)/(k+3r)
(
q
+
r
)
/
(
k
+
3
r
)
\newline
B) Cannot be simplified
\newline
C)
(
a
+
r
)
(
q
−
3
r
)
(a+r)(q-3r)
(
a
+
r
)
(
q
−
3
r
)
\newline
D)
(
q
+
r
)
(
q
+
3
r
)
(q+r)(q+3r)
(
q
+
r
)
(
q
+
3
r
)
Get tutor help
Which value of
v
v
v
makes
12
=
12
+
v
−
8
2
12=12+\frac{v-8}{2}
12
=
12
+
2
v
−
8
a true statement?
\newline
Choose
1
1
1
answer:
\newline
(A)
v
=
8
v=8
v
=
8
\newline
(B)
v
=
10
v=10
v
=
10
\newline
(C)
v
=
12
v=12
v
=
12
\newline
(D)
v
=
14
v=14
v
=
14
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Factorise
48
a
4
−
243
b
4
48a^4-243b^4
48
a
4
−
243
b
4
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Factorise
x
4
−
y
4
x^{4}-y^{4}
x
4
−
y
4
.
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x
3
+
9
x
2
x
3
\frac{x^3+9x^2}{x^3}
x
3
x
3
+
9
x
2
which expression is equivalent to the given expression for all
x
>
1
x>1
x
>
1
?
\newline
(A)
9
x
2
9x^2
9
x
2
\newline
(B)
1
+
9
x
2
1+9x^2
1
+
9
x
2
\newline
(C)
x
+
9
x
x+\frac{9}{x}
x
+
x
9
\newline
(D)
1
+
9
x
x
1+\frac{9x}{x}
1
+
x
9
x
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Simplify the expression below and write your final expression.
\newline
6
x
2
−
384
2
x
2
−
36
x
+
160
⋅
x
−
10
x
2
+
12
x
+
32
\frac{6 x^{2}-384}{2 x^{2}-36 x+160} \cdot \frac{x-10}{x^{2}+12 x+32}
2
x
2
−
36
x
+
160
6
x
2
−
384
⋅
x
2
+
12
x
+
32
x
−
10
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simplify the following
(
p
+
q
)
2
−
36
q
2
2
p
2
−
50
q
2
(p+q)^2 - \frac{36q^2}{2p^2} - 50q^2
(
p
+
q
)
2
−
2
p
2
36
q
2
−
50
q
2
Get tutor help
Factorise:
\newline
(
3
x
−
4
y
)
4
−
x
4
(3x - 4y)^4 - x^4
(
3
x
−
4
y
)
4
−
x
4
Get tutor help
Simplify
\newline
2
3
+
2
−
3
2^{3}+2^{-3}
2
3
+
2
−
3
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Simplify
6
2
3
+
6
−
4
3
6
+
2
+
2
6
2
+
3
\frac{6 \sqrt{2}}{\sqrt{3}+\sqrt{6}}-\frac{4 \sqrt{3}}{\sqrt{6}+\sqrt{2}}+\frac{2 \sqrt{6}}{\sqrt{2}+\sqrt{3}}
3
+
6
6
2
−
6
+
2
4
3
+
2
+
3
2
6
Get tutor help
Select all the expressions that are equivalent to
(
1
1
3
)
0
(11^3)^0
(
1
1
3
)
0
.
\newline
Multi-select Choices:
\newline
(A)
1
1
1
\newline
(B)
1
1
0
11^0
1
1
0
\newline
(C)
11
11
11
\newline
(D)
1
1
1
0
\frac{1}{11^0}
1
1
0
1
Get tutor help
Select all the expressions that are equivalent to
8
5
4
5
\frac{8^5}{4^5}
4
5
8
5
.
\newline
Multi-select Choices:
\newline
(A)
1
2
5
\frac{1}{2^5}
2
5
1
\newline
(B)
1
2
−
5
\frac{1}{2^{-5}}
2
−
5
1
\newline
(C)
2
2
2
\newline
(D)
2
5
2^5
2
5
Get tutor help
Select all the expressions that are equivalent to
8
7
×
8
6
8^7 \times 8^6
8
7
×
8
6
.
\newline
Multi-select Choices:
\newline
(A)
1
8
13
\frac{1}{8^{13}}
8
13
1
\newline
(B)
1
8
42
\frac{1}{8^{42}}
8
42
1
\newline
(C)
8
42
8^{42}
8
42
\newline
(D)
1
8
−
13
\frac{1}{8^{-13}}
8
−
13
1
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Select all the expressions that are equivalent to
1
2
2
/
2
2
12^2/2^2
1
2
2
/
2
2
.
\newline
Multi-select Choices:
\newline
(A)
1
/
6
−
2
1/6^{-2}
1/
6
−
2
\newline
(B)
6
2
6^2
6
2
\newline
(C)
6
6
6
\newline
(D)
6
0
6^0
6
0
Get tutor help
Select all the expressions that are equivalent to
(
5
4
)
2
(5^4)^2
(
5
4
)
2
.
\newline
Multi-select Choices:
\newline
(A)
1
5
8
\frac{1}{5^8}
5
8
1
\newline
(B)
5
6
5^6
5
6
\newline
(C)
5
8
5^8
5
8
\newline
(D)
1
5
6
\frac{1}{5^6}
5
6
1
Get tutor help
Select all the expressions that are equivalent to
6
5
3
5
\frac{6^5}{3^5}
3
5
6
5
.
\newline
Multi-select Choices:
\newline
(A)
1
2
5
\frac{1}{2^5}
2
5
1
\newline
(B)
1
2
−
5
\frac{1}{2^{-5}}
2
−
5
1
\newline
(C)
2
2
2
\newline
(D)
2
0
2^0
2
0
Get tutor help
Select all the expressions that are equivalent to
1
2
5
3
5
\frac{12^5}{3^5}
3
5
1
2
5
.
\newline
Multi-select Choices:
\newline
(A)
1
4
5
\frac{1}{4^5}
4
5
1
\newline
(B)
4
5
4^5
4
5
\newline
(C)
4
4
4
\newline
(D)
4
0
4^0
4
0
Get tutor help
Select all the expressions that are equivalent to
5
5
×
5
9
5^5 \times 5^9
5
5
×
5
9
.
\newline
Multi-select Choices:
\newline
(A)
1
5
14
\frac{1}{5^{14}}
5
14
1
\newline
(B)
5
14
5^{14}
5
14
\newline
(C)
5
45
5^{45}
5
45
\newline
(D)
1
5
−
14
\frac{1}{5^{-14}}
5
−
14
1
Get tutor help
Select all the expressions that are equivalent to
6
4
×
6
8
6^4 \times 6^8
6
4
×
6
8
.
\newline
Multi-select Choices:
\newline
(A)
1
6
32
\frac{1}{6^{32}}
6
32
1
\newline
(B)
6
12
6^{12}
6
12
\newline
(C)
6
32
6^{32}
6
32
\newline
(D)
1
6
−
12
\frac{1}{6^{-12}}
6
−
12
1
Get tutor help
Find both solutions to the equation.
\newline
100
+
(
n
−
2
)
2
=
116
100+(n-2)^{2}=116
100
+
(
n
−
2
)
2
=
116
Get tutor help
x
−
2
(
x
+
2
)
(
x
+
1
)
\frac{x-2}{(x+2)(x+1)}
(
x
+
2
)
(
x
+
1
)
x
−
2
=
Get tutor help
Simplify using Factorization:
(
65
y
3
(
50
y
2
−
98
)
)
/
(
26
y
2
(
5
y
+
7
)
)
(65y^3(50y^2-98))/(26y^2(5y+7))
(
65
y
3
(
50
y
2
−
98
))
/
(
26
y
2
(
5
y
+
7
))
Get tutor help
Simplify using Factorization:
(
39
y
3
(
50
y
2
−
98
)
)
/
(
52
y
2
(
5
y
+
7
)
)
(39y^3(50y^2-98))/(52y^2(5y+7))
(
39
y
3
(
50
y
2
−
98
))
/
(
52
y
2
(
5
y
+
7
))
Get tutor help
If
j
k
=
4
5
\frac{j}{k}=\frac{4}{5}
k
j
=
5
4
, which of the following correctly expresses
k
k
k
in terms of
j
j
j
?
\newline
Choose
1
1
1
answer:
\newline
(A)
k
=
4
5
j
k=\frac{4}{5 j}
k
=
5
j
4
\newline
(B)
k
=
5
4
j
k=\frac{5}{4 j}
k
=
4
j
5
\newline
(C)
k
=
4
j
5
k=\frac{4 j}{5}
k
=
5
4
j
\newline
(D)
k
=
5
j
4
k=\frac{5 j}{4}
k
=
4
5
j
Get tutor help
Simplify.
7
v
−
21
v
−
3
⋅
v
+
10
7
v
−
42
\frac{7 v-21}{v-3} \cdot \frac{v+10}{7 v-42}
v
−
3
7
v
−
21
⋅
7
v
−
42
v
+
10
Get tutor help
5
+
4
m
2
+
7
m
−
m
2
+
3
m
−
13
5+4 m^{2}+7 m-m^{2}+3 m-13
5
+
4
m
2
+
7
m
−
m
2
+
3
m
−
13
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
3
m
−
4
)
(
m
+
2
)
(3 m-4)(m+2)
(
3
m
−
4
)
(
m
+
2
)
\newline
(B)
(
3
m
+
4
)
(
m
−
2
)
(3 m+4)(m-2)
(
3
m
+
4
)
(
m
−
2
)
\newline
(C)
(
3
m
−
2
)
(
m
+
4
)
(3 m-2)(m+4)
(
3
m
−
2
)
(
m
+
4
)
\newline
(D)
(
3
m
+
2
)
(
m
−
4
)
(3 m+2)(m-4)
(
3
m
+
2
)
(
m
−
4
)
Get tutor help
Simplify the expression to a + bi form:
\newline
(
2
−
9
i
)
2
(2-9 i)^{2}
(
2
−
9
i
)
2
\newline
Answer:
Get tutor help
Which expression is equivalent to
3
w
+
3
w
3w + 3w
3
w
+
3
w
?
\newline
Choices:
\newline
(A)
w
6
w^6
w
6
\newline
(B)
6
w
6w
6
w
\newline
(C)
w
+
6
w + 6
w
+
6
\newline
(D)
5
w
5w
5
w
Get tutor help
Which expression is equivalent to
2
n
+
3
n
2n + 3n
2
n
+
3
n
?
\newline
Choices:
\newline
(A)
n
+
5
n + 5
n
+
5
\newline
(B)
n
5
n^5
n
5
\newline
(C)
4
n
4n
4
n
\newline
(D)
5
n
5n
5
n
Get tutor help
Which expression is equivalent to
2
z
+
z
2z + z
2
z
+
z
?
\newline
Choices:
\newline
(A)
4
z
4z
4
z
\newline
(B)
z
3
z^3
z
3
\newline
(C)
3
z
3z
3
z
\newline
(D) $z + \(3\)
Get tutor help
Which expression is equivalent to
2
w
+
w
2w + w
2
w
+
w
?
\newline
Choices:
\newline
(A)
w
3
w^3
w
3
\newline
(B)
w
+
3
w + 3
w
+
3
\newline
(C)
2
w
2w
2
w
\newline
(D)
3
w
3w
3
w
Get tutor help
Which expression is equivalent to
9
w
+
7
w
9w + 7w
9
w
+
7
w
?
\newline
Choices:
\newline
(A)
16
w
16w
16
w
\newline
(B)
w
16
w^{16}
w
16
\newline
(C)
w
+
16
w + 16
w
+
16
\newline
(D)
15
w
15w
15
w
Get tutor help
Which expression is equivalent to
4
t
+
t
4t + t
4
t
+
t
?
\newline
Choices:
\newline
(A)
5
t
5t
5
t
\newline
(B)
t
5
t^5
t
5
\newline
(C)
t
+
5
t + 5
t
+
5
\newline
(D)
6
t
6t
6
t
Get tutor help
Which expression is equivalent to
8
k
+
8
k
8k + 8k
8
k
+
8
k
?
\newline
Choices:
\newline
(A)
k
16
k^{16}
k
16
\newline
(B)
17
k
17k
17
k
\newline
(C)
16
k
16k
16
k
\newline
(D)
k
+
16
k + 16
k
+
16
Get tutor help
Which expression is equivalent to
8
u
+
6
u
8u + 6u
8
u
+
6
u
?
\newline
Choices:
\newline
(A)
14
u
14u
14
u
\newline
(B)
15
u
15u
15
u
\newline
(C)
u
14
u^{14}
u
14
\newline
(D)
u
+
14
u + 14
u
+
14
Get tutor help
Which expression is equivalent to
4
g
+
g
4g + g
4
g
+
g
?
\newline
Choices:
\newline
(A)
4
g
4g
4
g
\newline
(B)
g
5
g^5
g
5
\newline
(C)
5
g
5g
5
g
\newline
(D)
g
+
5
g + 5
g
+
5
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Which expression is equivalent to
5
d
+
9
d
5d + 9d
5
d
+
9
d
?
\newline
Choices:
\newline
(A)
d
+
14
d + 14
d
+
14
\newline
(B)
d
14
d^{14}
d
14
\newline
(C)
15
d
15d
15
d
\newline
(D)
14
d
14d
14
d
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Which expression is equivalent to
3
d
+
6
d
3d + 6d
3
d
+
6
d
?
\newline
Choices:
\newline
(A)
d
9
d^9
d
9
\newline
(B)
10
d
10d
10
d
\newline
(C)
9
d
9d
9
d
\newline
(D)
d
+
9
d + 9
d
+
9
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Which expression is equivalent to
5
x
+
2
x
5x + 2x
5
x
+
2
x
?
\newline
Choices:
\newline
(A)
7
x
7x
7
x
\newline
(B)
x
7
x^7
x
7
\newline
(C)
8
x
8x
8
x
\newline
(D)
x
+
7
x + 7
x
+
7
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Which expression is equivalent to
5
u
+
4
u
5u + 4u
5
u
+
4
u
?
\newline
Choices:
\newline
(A)
u
+
9
u + 9
u
+
9
\newline
(B)
u
9
u^9
u
9
\newline
(C)
9
u
9u
9
u
\newline
(D)
8
u
8u
8
u
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Which expression is equivalent to
6
u
+
9
u
6u + 9u
6
u
+
9
u
?
\newline
Choices:
\newline
(A)
u
+
15
u + 15
u
+
15
\newline
(B)
u
15
u^{15}
u
15
\newline
(C)
15
u
15u
15
u
\newline
(D)
16
u
16u
16
u
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Which expression is equivalent to
9
(
4
q
)
9(4q)
9
(
4
q
)
?
\newline
Choices:
\newline
(A)
q
+
13
q + 13
q
+
13
\newline
(B)
q
+
36
q + 36
q
+
36
\newline
(C)
4
q
+
9
4q + 9
4
q
+
9
\newline
(D)
36
q
36q
36
q
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Which expression is equivalent to
6
c
+
4
c
6c + 4c
6
c
+
4
c
?
\newline
Choices:
\newline
(A)
c
+
10
c + 10
c
+
10
\newline
(B)
10
c
10c
10
c
\newline
(C)
9
c
9c
9
c
\newline
(D)
c
10
c^{10}
c
10
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