Exponents And Powers

Question

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Say true or false and justify your answer:
(i) 10 × 10¹¹ = 100¹¹ (ii) 2³ > 5²
(iii) 2³ × 3² = 6⁵(iv) 3⁰ = (1000)⁰

Solution

(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.

Some More Questions From Exponents and Powers Chapter

Simplify:
(i) 2 × 10³ (ii) 7² × 2²
(iii) 2³ × 5 (iv) 3 × 4⁴
(v) 0 × 10² (vi) 5² × 3³
(vii) 2⁴× 3² (viii) 3² × 10⁴

Simplify:
(i) (− 4)³
(ii) (− 3) × (− 2)³
(iii) (− 3)² × (− 5)²
(iv)(− 2)³ × (−10)³

Compare the following numbers:
(i) 2.7 × 10¹²; 1.5 × 10⁸
(ii) 4 × 10¹⁴; 3 × 10¹⁷