EXPRESS A NUMBER IN INDEX FORM

To express the given number in index form, we have to decompose the number as prime factors.

If we have repeated values, using exponents we can write down it.

For example,

5 x 5 x 5 = 53

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

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