Say true or false and justify your answer:
(i) 10 × 1011 = 10011
(ii) 23 > 52
(iii) 23 × 32 = 65
(iv) 30 = (1000)0
(i) We have,
10 × 1011 = 10011
L.H.S. = 10 × 1011
Using identity: (am × an = am + n)
= 1011 + 1
= 1012
R.H.S. = 10011
= (10 × 10)11
= (102)11
Using identity: (am)n = amn
= 102 × 11
= 1022
So, it is clear that
L.H.S. 
R.H.S.
∴ The statement given in the question is false
(ii) We have,
23 > 52
L.H.S. = 23
= 2 × 2 × 2
= 8
R.H.S. = 52
= 5 × 5
= 25
Since,
It is clear that 25 > 8
∴ The statement given in the question is false
(iii) We have,
23 × 32 = 65
L.H.S. = 23 × 32
= 2 × 2 × 2 × 3 × 3
= 72
R.H.S. = 65
= 6 × 6 × 6 × 6 × 6
= 7776
It is clear that
L.H.S. 
R.H.S.
∴ The statement given in the question is false
(iv) We have,
30 = (1000)0
L.H.S. = 30
= 1
R.H.S. = (1000)0
= 1
Hence,
L.H.S. = R.H.S.
∴ The statement given in the question is true