EXPRESS A NUMBER IN INDEX FORM

Express the following as the product of prime factors in index form:

Problem 1 :

56

Solution :

56 = 8 × 7

= 2 × 2 × 2 × 7

= 2³ × 7

Problem 2 :

240

Solution :

240 = 16 × 15

= 4 × 4 × 3 × 5

= 2 × 2 × 2 × 2 × 3 × 5

= 2⁴ × 3 × 5

Problem 3 :

504

Solution :

504 = 72 × 7

= 8 × 9 × 7

= 2 × 2 × 2 × 3 × 3 × 7

= 2³ × 3² × 7

Problem 4 :

735

Solution :

735 = 15 × 49

= 3 × 5 × 7 × 7

= 3 × 5 × 7²

Problem 5 :

297

Solution :

 297 = 27 × 11

= 9 × 3 × 11

= 3 × 3 × 3 × 11

= 3³ × 11

Problem 6 :

221

Solution :

221 = 13 × 17

Problem 7 :

360

Solution :

360 = 72 × 5

= 8 × 9 × 5

= 2 × 2 × 2 × 3 × 3 × 5

= 2³ × 3² × 5

Problem 8 :

952

Solution :

952 = 56 × 17

= 8 × 7 × 17

= 2 × 2 × 2 × 7 × 17

= 2³ × 7 × 17