Question

Write the following in exponential form using prime factorization. 

i) 2500 

ii) 1296 

iii) 8000 

iv) 6300

Answer 1

i) 2500 = 2 × 1250 = 2 × 2 × 625

= (2 × 2) × 5 × 125

= (2 × 2) × 5 × 5 × 25

= (2 × 2) × (5 × 5 × 5 × 5)

= 2² × 5⁴

ii) 1296 = 2 × 648 = 2 × 2 × 324 = 2 × 2 × 2 × 162

= (2 × 2 × 2 × 2) × 81

= (2 × 2 × 2 × 2 ) ×  3 × 27

= (2 × 2 × 2 × 2 ) × 3 × 3 × 9

= (2 × 2 × 2 × 2 ) × ( 3 × 3 × 3 × 3 )

= 2⁴ × 3⁴

iii) 8000 = 2 × 4000 = 2 × 2 × 2000 

= 2 × 2 × 2 × 1000

= 2 × 2 × 2 × 2 × 500

= 2 × 2 × 2 × 2 × 2 × 250

= (2 × 2 × 2 × 2 × 2 × 2) × 125

= (2 × 2 × 2 × 2 × 2 × 2) × 5 × 25

= (2 × 2 × 2 × 2 × 2 × 2) × ( 5 × 5 × 5)

= (2⁶ × 5³)

iv) 6300 = 2 × 3150 = 2 × 2 × 1575

= (2 × 2) × 3 × 525

= 2 × 2 × 3 × 3 × 175

= (2 × 2) × (3 × 3) × 5 × 35

= (2 × 2) × (3 × 3) × (5 × 5) × 7

= 2² × 3² × 5² × 7