Question

Say true or false and justify your answer:

(i) 10 × 10¹¹ = 100¹¹ (ii) 2³ > 5²

(iii) 2³ × 3² = 6⁵ (iv) 3⁰ = (1000)⁰

Answer 1

(i) 10 × 10¹¹ = 100¹¹

L.H.S. = 10 × 10¹¹ = 10^{11 + 1} (a^m × aⁿ = a^m+n)

= 10¹²

R.H.S. = 100¹¹ = (10 ×10)¹¹= (10²)¹¹

= 10^{2 × 11} = 10²² (a^m)ⁿ = a^mn

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.