Identify the greater number, wherever possible, in each of the following.
(i) 43 or 34
(ii) 53 or 35
(iii) 28 or 82
(iv) 1002 or 2100
(v) 210 or 102
(i) We have, 43 or 34
On simplifying we get,
43 = 4 × 4 × 4
= 64
And,
34 = 3 × 3 × 3 × 3
= 81
Clearly,
81 > 64
Thus,
34 > 43
(ii) We have, 53 or 35
On simplifying we get,
53 = 5 × 5 × 5
= 125
35 = 3 × 3 × 3 × 3 × 3
= 243
Clearly,
243 > 125
Thus,
35 > 53
(iii) We have, 28 or 82
On simplifying we get,
28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 256
82 = 8 × 8
= 64
Clearly,
256 > 64
Thus,
28 > 82
(iv) We have, 1002 or 2100
On simplifying we get,
1002 = 100 × 100
= 10000
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 1024
Now,
2100 = 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024
Clearly,
2100 > 10000
Thus,
2100 > 1002
(v) W have, 210 or 102
On simplifying we get,
102 = 10 × 10
= 100
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 1024
Clearly,
1024 > 100
Thus,
210 > 102