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Number System: Exponent Test-2

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Your answers are highlighted below.
Question 1
0.96/(0.3)-3 = ?
A
3/(15)9
B
0.000009/0.003
C
315/109
D
9.009/0.333
Question 1 Explanation: 
0.96/(0.3)-3
= (0.9)6 (0.3)3
= (96/106) x (33/103)
= (3(2)6/106) x (33/103)
= (312/106) x (33/103)
= (315/109)
Question 2
If 34 = 9x, then x = ?
A
.2
B
4
C
.6
D
8
Question 2 Explanation: 
34 = 9x
34 = 32x
2x = 4
x =2
Question 3
If 9x/(32+32+32)=1/81, then what is the value of x?
A
-2
B
-3
C
-4
D
5
Question 3 Explanation: 
9x/(3x+3x+3x)=1/81
32x/(3x+3x+3x)=1/81
32x/3x(3)=1/81
32x/3x(3)=1/81
3x/(3)=1/81 so x = -3
Question 4
If p = 729–4/3 x 3243/2 x 81/3,  then what will be the value of p1/2?
A
4/3
B
9/4
C
16/81
D
3/2
Question 4 Explanation: 
p=729–4/3 x 3243/2 x 81/3
p=93(–4/3) x 18 2(3/2) x 2
p= 9–4 x 183 x 2
p= 16/9
p1/2=4/3
that is, option a
Question 5
If  (64)1/2m = 22m then what will be the value of m
A
+3/4
B
–1/4
C
0
D
$ \sqrt{\frac{3}{2}}$
Question 5 Explanation: 
(64)1/2m = 22m
(82)1/2m  = 22m
(82 )1/2m= 22m
(8 )1/m= 22m
(23)1/m = 22m
3/m = 2m
2m2 = 3
m2 = 3/2
m = $ \sqrt{\frac{3}{2}}$
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