EduSahara™ Assignment
Name : Equations involving Base Powers
Chapter : Exponents and Powers
Grade : SSC Grade VIII
License : Non Commercial Use
Question
1
1.
If
3
x
=
243
, find
x
(i)
8
(ii)
4
(iii)
3
(iv)
6
(v)
5
Question
2
2.
If
3
v
=
27
, find
8
v
(i)
515
(ii)
513
(iii)
511
(iv)
512
(v)
509
Question
3
3.
If
3
(
7
t
+
1
)
=
9
(
3
t
+
5
)
, find
t
(i)
7
(ii)
12
(iii)
10
(iv)
9
(v)
8
Question
4
4.
If
243
(
k
+
1
)
=
27
(
2
k
+
1
)
, find
k
(i)
1
(ii)
5
(iii)
3
(iv)
(-1)
(v)
2
Question
5
5.
If
9
(
v
+
3
)
=
81
8
=
3
w
, find
w
(i)
34
(ii)
31
(iii)
33
(iv)
32
(v)
30
Question
6
6.
If
2
k
=
4
, find
2
(
k
+
3
)
(i)
32
(ii)
31
(iii)
29
(iv)
34
(v)
33
Question
7
7.
If
(
8
16
)
15
=
(
8
3
)
a
, find
a
(i)
79
(ii)
83
(iii)
81
(iv)
78
(v)
80
Question
8
8.
If
625
✕
5
s
=
5
9
, find
s
(i)
5
(ii)
7
(iii)
6
(iv)
3
(v)
4
Question
9
9.
If
10
(
2
v
+
2
)
÷
1000
=
10
7
, find
v
(i)
6
(ii)
1
(iii)
4
(iv)
3
(v)
5
Question
10
10.
Which of the following statements are true?
a)
a
.
x
m
=
a
m
.
x
m
b)
a
0
=
1
(
a
≠
0)
c)
(
x
m
)
n
=
x
(
m
+
n
)
d)
x
m
x
n
=
x
m
n
e)
(
x
m
)
n
=
(
x
n
)
m
f)
a
m
.
a
n
=
a
m
n
(i)
{b,e}
(ii)
{c,e}
(iii)
{a,e,b}
(iv)
{a,b}
(v)
{d,f,b}
Question
11
11.
If
a
x
=
b
,
b
y
=
c
and
c
z
=
a
, then
x
y
z
=
(i)
(
a
+
b
+
c
)
(ii)
-1
(iii)
a
b
c
(iv)
0
(v)
1
Question
12
12.
If
c
u
=
d
v
=
e
w
=
f
x
and
c
d
=
e
f
, then
(i)
v
w
=
u
x
(ii)
1
v
+
1
x
=
1
w
+
1
u
(iii)
v
u
=
w
x
(iv)
1
v
+
1
u
=
1
w
+
1
x
(v)
1
v
+
1
w
=
1
u
+
1
x
Question
13
13.
If
f
(
v
−
1
)
=
g
h
,
g
(
w
−
1
)
=
h
f
,
h
(
x
−
1
)
=
f
g
then
a)
(
v
+
w
+
x
)
=
1
b)
v
w
+
w
x
+
x
v
=
0
c)
v
w
+
w
x
+
x
v
=
1
d)
v
w
x
=
1
e)
v
w
+
w
x
+
x
v
=
v
w
x
(i)
{c,d,e}
(ii)
{e}
(iii)
{a,e}
(iv)
{b,e}
Question
14
14.
Simplify
(
v
i
v
j
)
(
i
+
j
)
(
v
j
v
k
)
(
j
+
k
)
(
v
k
v
i
)
(
k
+
i
)
(i)
v
(ii)
-1
(iii)
0
(iv)
1
(v)
v
(
i
+
j
+
k
)
Question
15
15.
Simplify
(
z
d
)
(
e
−
f
)
(
z
e
)
(
f
−
d
)
(
z
f
)
(
d
−
e
)
(i)
1
(ii)
z
(
d
+
e
+
f
)
(iii)
-1
(iv)
0
(v)
z
Question
16
16.
Simplify
(
w
(
b
+
c
)
)
(
b
−
c
)
(
w
(
c
+
d
)
)
(
c
−
d
)
(
w
(
d
+
b
)
)
(
d
−
b
)
(i)
0
(ii)
-1
(iii)
w
(iv)
1
(v)
w
(
b
+
c
+
d
)
Question
17
17.
Simplify
(
w
h
w
i
)
j
(
w
i
w
j
)
h
(
w
j
w
h
)
i
(i)
1
(ii)
w
(iii)
w
(
h
+
i
+
j
)
(iv)
0
(v)
-1
Question
18
18.
Simplify
(
8
j
.
81
(
j
−
2
)
.
100
(
j
−
1
)
64
(
j
−
2
)
.
9
(
j
−
1
)
.
10
(
j
−
4
)
)
(i)
8
(
−
j
+
4
)
.
9
(
−
j
)
.
10
(
−
j
+
7
)
(ii)
8
(
−
j
+
4
)
.
9
(
j
−
3
)
.
10
(
j
+
2
)
(iii)
8
2
.
9
(
−
1
)
.
10
3
(iv)
8
(
j
+
2
)
.
9
(
−
j
)
.
10
(
−
j
+
7
)
Question
19
19.
(
b
(-2)
+
c
(-2)
)
0
=
(i)
b
(-2)
+
c
(-2)
(ii)
(-2)
(iii)
0
(iv)
4
(v)
1
Assignment Key
1) (v)
2) (iv)
3) (iv)
4) (v)
5) (iv)
6) (i)
7) (v)
8) (i)
9) (iii)
10) (i)
11) (v)
12) (iv)
13) (ii)
14) (iv)
15) (i)
16) (iv)
17) (i)
18) (ii)
19) (v)
