Question

Express each of the following as a product of prime factors only in exponential form:
(i) 108 × 192 (ii) 270 (iii) 729 × 64 (iv) 768

Answer 1

(i) 108 x 192
= (2 x 2 x 3 x 3 x 3) x (2 x 2 x 2 x 2 x 2 x 2 x 3)
= (22 x 33 ) x (26 x 3)
= 26 + 2 x 33 + 1 (am x an = am+n)
= 28 x 34

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(ii) 270
= 2 x 3 x 3 x 3 x 5
= 2 x 33 x 5

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(iii) 729 x 64
= (3 x 3 x 3 x 3 x 3 x 3) x (2 x 2 x 2 x 2 x 2 x 2)
= 36 x 26

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(iv) 768
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3
= 28 x 3