Question

Express the following as the product of exponents through prime factorization.

(i) 288

(ii) 1250

(iii) 2250

(iv) 3600

(v) 2400

Answer 1

(i) 288

1) 288 = 2 × 144

= 2 × 2 × 72

= 2 × 2 × 2 × 36

= 2 × 2 × 2 × 2 × 18

= 2 × 2 × 2 × 2 × 2 × 9

= (2 × 2 × 2 × 2× 2) × (3 × 3)

= 2⁵ × 3²

(ii) 1250 = 2 × 625

= 2 × 5 × 125

= 2 × 5 × 5 × 25

= 2 × 5 × 5 × 5 × 5

= 2 × 5⁴

(iii) 2250 = 2 × 1125

= 2 × 3 × 375

= 2 × 3 × 3 × 125

= 2 × 3 × 3 × 5 × 25

= 2 × 3 × 3 × 5 × 5 × 5

= 2¹ × 3² × 5³

(iv) 3600 = 2 × 1800

= 2 × 2 × 900

=2 × 2 × 2 × 450

=2 × 2 × 2 × 2 × 225

= ( 2 × 2 × 2 × 2 ) × 3 × 75

= (2 × 2 × 2 × 2) × (3 × 3) × 25

= (2 × 2 × 2 × 2) × (3 × 3) × (5 × 5)

= 2⁴ × 3² × 5²

(v) 2400

2400 = 2 × 1200

= 2 × 2 × 600

= 2 × 2 × 2 × 300

= 2 × 2 × 2 × 2 × 150

= 2 × 2 × 2 × 2 × 2 × 75

= (2 × 2 × 2 × 2 × 2) × 3 × 25

= (2 × 2 × 2 × 2 × 2) × 3 × (5 × 5)

= 2⁵ × 3¹