Compare the following numbers:

(i) 2.7 × 10¹²; 1.5 × 10⁸

(ii) 4 × 10¹⁴; 3 × 10¹⁷

Express the following numbers using exponential notation:

(i) 512 (ii) 343

(iii) 729 (iv) 3125

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

Express each of the following as product of powers of their prime factors:

(i) 648 (ii) 405

(iii) 540 (iv) 3,600

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

Say true or false and justify your answer:

(i) 10 × 10¹¹ = 100¹¹ (ii) 2³ > 5²

(iii) 2³ × 3² = 6⁵ (iv) 3⁰ = (1000)⁰

Express each of the following as a product of prime factors only in exponential form:

(i) 108 × 192 (ii) 270

(iii) 729 × 64 (iv) 768