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Question

Say true or false and justify your answer:

(i) 10 × 1011 = 10011 (ii) 23 > 52

(iii) 23 × 32 = 65 (iv) 30 = (1000)0

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Solution

(i) 10 × 1011 = 10011

L.H.S. = 10 × 1011 = 1011 + 1 (am × an = am+n)

= 1012

R.H.S. = 10011 = (10 ×10)11= (102)11

= 102 × 11 = 1022 (am)n = amn

As L.H.S. ≠ R.H.S.,

Therefore, the given statement is false.

(ii) 23 > 52

L.H.S. = 23 = 2 × 2 × 2 = 8

R.H.S. = 52 = 5 × 5 = 25

As 25 > 8,

Therefore, the given statement is false.

(iii) 23 × 32 = 65

L.H.S. = 23 × 32 = 2 × 2 × 2 × 3 × 3 = 72

R.H.S. = 65 = 7776

As L.H.S. ≠ R.H.S.,

Therefore, the given statement is false.

(iv) 30 = (1000)0

L.H.S. = 30 = 1

R.H.S. = (1000)0 = 1 = L.H.S.

Therefore, the given statement is true.


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