Express each of the following numbers as a product of powers of their prime factors:
(i) 450
(ii) 2800
(iii) 24000

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Solution

We have
(i) Prime factorisation of 450 = 2 x 3 x 3 x 5 x 5 = 2 x 3² x 5²

(ii) Prime factorisation of 2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7 = 2⁴ x 5² x 7

(iii) Prime factorisation of 24000 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 = 2⁶ x 3 x 5³

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