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Number System: Exponent Test-1

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Question 1
(68-67)(69-68)=?
A
36
B
62
C
25 x 615
D
5 x 615
Question 1 Explanation: 
Using BODMAS and taking out the common powers from the bracket,
we are left with:
67(6-1)68(6-1)
6768(6-1) (6-1)
615 x 5 x 5
25 x 615
Question 2
What is the value of x if 810x-4 = 642x+4
A
1
B
2
C
3
D
4
Question 2 Explanation: 
Since the bases of the two sides are not equal, we first equate the bases.
We know  82=64
Therefore,
642x+4  =   8 2( 2x+4) =   8 4x+8
 Now let’s change our original equation:
 810x-4= 642x+4
 810x-4= 8 4x+8
Thus, 10x -4 = 4x + 8
6x = 12
x = 2
Question 3
What’s the largest value for x, so that 3x is a factor of 5412?
A
6
B
12
C
24
D
36
Question 3 Explanation: 
$ \begin{array}{l}Let\,us\,reduce\,the\,number\,{{54}^{{12}}}\operatorname{int}o\,\,factors\,\,of\,\,3\\{{54}^{{12}}}={{(2\times 27)}^{{12}}}\\={{(2\times 9\times 3)}^{{12}}}\\=\,\,{{(2\times 3\times 3\times 3)}^{{12}}}\\=\,\,({{2}^{{12}}}{{3}^{{12}}}{{3}^{{12}}}{{3}^{{12}}})\\=\,\,{{2}^{{12}}}{{3}^{{36}}}\end{array}$
Question 4
What is the value of 6.12 x 109?
A
0.00000000612
B
0.000000612
C
6.12
D
6120000000
Question 4 Explanation: 
This is a simple problem.
The number effectively becomes 612 x 107
. All you need to do is place seven zeros after the two.
Question 5
128146225/2253776115 = ?
A
2
B
3
C
6
D
12
Question 5 Explanation: 
The numerator reduces to:
2273876115
Dividing by
2253776115,
we obtain 2231, thus the correct answer is option D.
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