Express each of the following numbers as a product of powers of their prime factors:
(i) 36
(ii) 675
(iii) 392

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Solution

We have
(i) Prime factorisation of 36 = 2 x 2 x 3 x 3 = 2² x 3²

(ii) Prime factorisation of 675 = 3 x 3 x 3 x 5 x 5 = 3³ x 5²

(iii) Prime factorisation of 392 = 2 x 2 x 2 x 7 x 7 = 2³ x 7²

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