EduSahara™ Assignment
Name : Simplifying Expressions with Variables
Chapter : Indices
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
3
j
6
.
2
j
5
=
(i)
6
j
11
(ii)
5
j
30
(iii)
5
j
11
(iv)
6
j
30
(v)
11
j
6
Question
2
2.
2
m
8
.
8
m
8
.
9
m
6
=
(i)
22
m
144
(ii)
144
m
384
(iii)
19
m
384
(iv)
144
m
22
(v)
19
m
22
Question
3
3.
4
p
2
.
8
p
9
.
5
p
7
.
7
p
5
=
(i)
18
p
224
(ii)
224
p
90
(iii)
19
p
90
(iv)
1120
p
23
(v)
19
p
18
Question
4
4.
−
3
h
9
.
−
7
h
5
=
(i)
21
h
45
(ii)
−
10
h
14
(iii)
14
h
21
(iv)
−
10
h
45
(v)
21
h
14
Question
5
5.
−
8
g
(-4)
.
−
5
g
3
.
−
3
g
6
=
(i)
−
120
g
(-72)
(ii)
−
120
g
5
(iii)
5
g
(-120)
(iv)
−
16
g
5
(v)
−
16
g
(-72)
Question
6
6.
−
6
u
8
.
−
4
u
(-7)
.
−
5
u
(-4)
.
−
3
u
(-7)
=
(i)
360
u
(-10)
(ii)
−
13
u
(-3)
(iii)
−
72
u
392
(iv)
−
13
u
392
(v)
−
3
u
(-72)
Question
7
7.
Find the square root of
h
2
i
4
j
4
=
(i)
1
h
2
i
4
j
4
(ii)
(
h
2
i
4
j
4
)
2
(iii)
h
i
j
32
(iv)
h
i
2
j
2
(v)
h
i
j
10
Question
8
8.
2
q
3
r
(-3)
.
−
5
q
2
r
(-3)
=
(i)
−
10
q
5
r
(-6)
(ii)
−
3
q
5
r
(-6)
(iii)
10
q
5
(iv)
−
10
q
3
r
(-3)
(v)
7
q
5
r
(-6)
Question
9
9.
(
d
2
)
8
=
(i)
8
d
2
(ii)
d
16
(iii)
d
6
(iv)
d
10
(v)
d
2
Question
10
10.
w
13
w
5
=
(i)
5
w
8
(ii)
w
8
(iii)
13
w
8
(iv)
w
18
(v)
w
65
Question
11
11.
(
e
2
f
3
)
4
=
(i)
e
6
f
7
(ii)
4
e
2
f
3
(iii)
4
e
6
f
7
(iv)
4
e
8
f
12
(v)
e
8
f
12
Question
12
12.
(
−
2
x
6
y
3
)
4
=
(i)
16
x
24
y
12
(ii)
16
x
10
y
7
(iii)
−
8
x
24
y
12
(iv)
−
2
x
24
y
12
(v)
−
8
x
10
y
7
Question
13
13.
(
k
11
k
3
)
3
=
(i)
k
42
(ii)
k
24
(iii)
3
k
14
(iv)
k
99
(v)
3
k
8
Question
14
14.
(
s
6
t
8
u
5
)
7
=
(i)
(
s
42
t
56
u
12
)
(ii)
(
s
42
t
56
u
35
)
(iii)
(
s
13
t
15
u
12
)
(iv)
(
7
s
6
t
8
7
u
5
)
(v)
(
s
13
t
15
u
35
)
Question
15
15.
p
14
q
17
p
2
q
4
=
(i)
p
16
q
13
(ii)
p
16
q
21
(iii)
p
12
q
13
(iv)
p
31
q
6
(v)
p
12
q
21
Question
16
16.
s
8
s
14
=
(i)
1
s
(-6)
(ii)
s
6
(iii)
1
s
6
(iv)
1
s
22
(v)
1
s
112
Question
17
17.
(
c
3
)
(
d
+
3
)
=
(i)
c
(
3
d
+
9
)
(ii)
c
(
3
d
+
6
)
(iii)
c
(
d
+
12
)
(iv)
c
(
3
d
−
9
)
(v)
c
(
d
+
9
)
Question
18
18.
(
n
7
o
3
)
p
=
(i)
o
3
p
n
7
p
(ii)
n
7
p
.
−
o
3
p
(iii)
n
7
p
o
3
p
(iv)
n
7
p
.
o
3
p
Question
19
19.
(
q
(
−
10
s
+
4
)
q
(
6
s
+
8
)
)
=
(i)
q
(
−
4
s
+
12
)
(ii)
q
(
−
16
s
−
3
)
(iii)
q
(
−
4
)
(iv)
q
(
16
s
2
−
38
s
−
8
)
(v)
q
(
−
16
s
−
4
)
Question
20
20.
(
h
5
h
5
)
5
=
(i)
h
10
(ii)
5
h
0
(iii)
h
0
(iv)
h
5
(v)
h
5
Question
21
21.
(
p
15
p
)
5
=
(i)
p
(
15
p
+
5
)
(ii)
p
15
p
(iii)
p
75
p
(iv)
5
p
75
p
Question
22
22.
(
q
(-3)
.
r
2
)
3
=
(i)
q
(-9)
.
r
6
(ii)
q
(-9)
.
r
4
(iii)
q
(-6)
.
r
6
(iv)
1
.
r
5
(v)
q
(-6)
.
r
(-1)
Question
23
23.
(
(
f
2
)
4
)
8
=
(i)
f
64
(ii)
f
(-10)
(iii)
1
(iv)
f
14
(v)
f
16
Question
24
24.
(
q
4
.
3
r
(-1)
)
-3
=
(i)
r
3
27
q
12
(ii)
r
3
.
27
q
(-12)
(iii)
−
3
r
3
−
9
q
(-12)
(iv)
r
3
3
q
(-12)
(v)
q
3
27
r
(-12)
Question
25
25.
(
w
+
x
)
(-4)
.
(
w
+
x
)
(-8)
=
(i)
(
w
+
x
)
32
(ii)
(
w
+
x
)
(-12)
(iii)
(
w
+
x
)
(-8)
(iv)
(
w
+
x
)
4
(v)
(
w
+
x
)
(-4)
Question
26
26.
(
e
3
3
f
3
)
-2
=
(i)
9
f
6
e
6
(ii)
9
e
f
(iii)
e
(-6)
9
f
(-6)
(iv)
9
e
(-6)
f
3
(v)
e
9
f
Question
27
27.
√
n
6
4
o
8
=
(i)
o
4
2
n
3
(ii)
n
3
2
o
4
(iii)
n
12
2
o
16
(iv)
2
n
3
o
4
(v)
n
6
2
o
8
Question
28
28.
Find the square root of
f
6
g
8
4
h
4
(i)
f
3
g
4
2
h
4
(ii)
f
6
g
4
2
h
2
(iii)
f
3
g
4
2
h
2
(iv)
f
3
g
8
2
h
2
(v)
f
6
g
8
2
h
4
Question
29
29.
Find the square root of
9
k
8
25
l
6
(i)
3
k
4
5
l
3
(ii)
3
k
16
5
l
12
(iii)
3
k
4
5
l
6
(iv)
3
k
8
5
l
3
(v)
3
k
8
5
l
6
Question
30
30.
p
(-7)
3
q
(-6)
=
(i)
3
q
6
p
7
(ii)
q
6
3
p
7
(iii)
p
6
3
q
7
(iv)
3
q
(-6)
p
(-7)
(v)
q
(-6)
3
p
(-7)
Question
31
31.
Which of the following statements are true?
a)
(
x
m
)
n
=
(
x
n
)
m
b)
a
.
x
m
=
a
m
.
x
m
c)
a
0
=
1
(
a
≠
0)
d)
(
x
m
)
n
=
x
(
m
+
n
)
e)
x
m
x
n
=
x
m
n
f)
a
m
.
a
n
=
a
m
n
(i)
{b,a}
(ii)
{a,c}
(iii)
{e,f,a}
(iv)
{b,c,a}
(v)
{d,c}
Question
32
32.
Simplify
(
w
k
w
l
)
(
k
+
l
)
(
w
l
w
m
)
(
l
+
m
)
(
w
m
w
k
)
(
m
+
k
)
(i)
-1
(ii)
1
(iii)
0
(iv)
w
(
k
+
l
+
m
)
(v)
w
Question
33
33.
Simplify
(
t
g
)
(
h
−
i
)
(
t
h
)
(
i
−
g
)
(
t
i
)
(
g
−
h
)
(i)
1
(ii)
t
(
g
+
h
+
i
)
(iii)
t
(iv)
-1
(v)
0
Question
34
34.
Simplify
(
t
(
f
+
g
)
)
(
f
−
g
)
(
t
(
g
+
h
)
)
(
g
−
h
)
(
t
(
h
+
f
)
)
(
h
−
f
)
(i)
-1
(ii)
t
(iii)
0
(iv)
1
(v)
t
(
f
+
g
+
h
)
Question
35
35.
Simplify
(
v
b
v
c
)
d
(
v
c
v
d
)
b
(
v
d
v
b
)
c
(i)
0
(ii)
1
(iii)
v
(iv)
v
(
b
+
c
+
d
)
(v)
-1
Question
36
36.
Simplify
(
t
(
g
+
h
)
)
5
(
t
(
h
+
i
)
)
5
(
t
(
i
+
g
)
)
5
(
t
g
.
t
h
.
t
i
)
(i)
t
(
5
g
+
5
h
+
5
i
)
(ii)
t
(
4
g
+
4
h
+
4
i
)
(iii)
t
(
9
g
+
9
h
+
9
i
)
(iv)
t
g
.
t
h
.
t
i
(v)
t
(
10
g
+
10
h
+
10
i
)
Question
37
37.
Simplify
(
7
b
.
64
(
b
−
4
)
.
81
(
b
−
5
)
49
(
b
−
4
)
.
8
(
b
−
5
)
.
9
(
b
−
1
)
)
(i)
7
4
.
8
1
.
9
(
−
4
)
(ii)
7
(
−
b
+
8
)
.
8
(
−
b
+
6
)
.
9
(
−
b
−
3
)
(iii)
7
(
b
+
4
)
.
8
(
−
b
+
6
)
.
9
(
−
b
−
3
)
(iv)
7
(
−
b
+
8
)
.
8
(
b
−
3
)
.
9
(
b
−
9
)
Question
38
38.
If
k
1
3
+
l
1
3
+
m
1
3
= 0, then
(i)
(
k
+
l
+
m
)
=
3
k
1
3
l
1
3
m
1
3
(ii)
(
k
+
l
+
m
)
3
=
27
k
l
m
(iii)
(
k
+
l
+
m
)
=
3
k
l
m
(iv)
(
k
+
l
+
m
)
=
27
k
l
m
Question
39
39.
Find the square root of
a
(
6
v
+
6
)
.
b
6
v
.
c
(
6
v
−
6
)
(i)
a
(
3
v
+
3
)
.
b
3
v
.
c
(
3
v
−
3
)
(ii)
a
(
v
+
3
)
.
b
6
v
.
c
(
v
−
3
)
(iii)
a
(
3
v
−
3
)
.
b
3
v
.
c
(
3
v
+
3
)
(iv)
6
a
(
v
+
1
)
.
6
b
v
.
6
c
(
v
−
1
)
Question
40
40.
(
h
(-2)
+
i
(-2)
)
0
=
(i)
0
(ii)
3
(iii)
(-1)
(iv)
1
(v)
h
(-2)
+
i
(-2)
Question
41
41.
Evaluate
(
c
1
2
+
d
1
2
)
(
c
1
2
−
d
1
2
)
=
(i)
(
c
+
d
)
2
(ii)
1
(iii)
(
c
+
d
)
(iv)
0
(v)
(
c
−
d
)
Question
42
42.
Evaluate
(
c
1
3
+
d
1
3
)
(
c
2
3
−
c
1
3
d
1
3
+
d
2
3
)
=
(i)
c
+
d
(ii)
(
c
−
d
)
2
(iii)
(
c
+
d
)
2
(iv)
c
−
d
(v)
0
Question
43
43.
Evaluate
(
f
1
3
−
g
1
3
)
(
f
2
3
+
f
1
3
g
1
3
+
g
2
3
)
=
(i)
(
f
+
g
)
2
(ii)
f
−
g
(iii)
0
(iv)
(
f
−
g
)
2
(v)
f
+
g
Question
44
44.
(
p
1
3
+
q
1
3
+
r
1
3
)
(
p
2
3
+
q
2
3
+
r
2
3
−
p
1
3
q
1
3
−
q
1
3
r
1
3
−
r
1
3
p
1
3
)
=
(i)
(
p
−
q
−
r
)
(ii)
(
p
+
q
+
r
)
2
(iii)
p
+
q
+
r
−
3
r
1
3
p
1
3
q
1
3
(iv)
0
(v)
(
p
−
q
−
r
)
2
Question
45
45.
(
1
2
p
q
r
)
✕
(
7
q
2
r
5
)
✕
(
−
7
2
r
4
)
=
(i)
7
2
p
q
3
r
6
(ii)
−
49
4
p
q
3
r
10
(iii)
343
4
q
6
r
14
(iv)
−
49
4
p
q
7
r
11
(v)
49
8
r
10
p
q
5
Question
46
46.
Evaluate
(
c
2
+
d
2
)
(
c
4
−
c
2
d
2
+
d
4
)
=
(i)
c
6
+
d
6
(ii)
c
6
−
2
d
2
c
4
+
2
d
4
c
2
−
d
6
(iii)
c
6
+
2
d
2
c
4
+
2
d
4
c
2
+
d
6
(iv)
0
(v)
c
6
−
d
6
Question
47
47.
Evaluate
(
g
2
−
1
)
(
g
4
+
g
2
+
1
)
=
(i)
0
(ii)
g
6
−
1
(iii)
g
6
−
2
g
2
+
1
(iv)
g
6
+
2
g
4
−
1
(v)
g
6
+
2
g
4
+
2
g
2
+
1
Assignment Key
1) (i)
2) (iv)
3) (iv)
4) (v)
5) (ii)
6) (i)
7) (iv)
8) (i)
9) (ii)
10) (ii)
11) (v)
12) (i)
13) (ii)
14) (ii)
15) (iii)
16) (iii)
17) (i)
18) (iii)
19) (v)
20) (iii)
21) (iii)
22) (i)
23) (i)
24) (i)
25) (ii)
26) (i)
27) (ii)
28) (iii)
29) (i)
30) (ii)
31) (ii)
32) (ii)
33) (i)
34) (iv)
35) (ii)
36) (iii)
37) (iv)
38) (i)
39) (i)
40) (iv)
41) (v)
42) (i)
43) (ii)
44) (iii)
45) (ii)
46) (i)
47) (ii)
