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)
= 2^{6 + 2} x 3^{3 + 1} (a^m x aⁿ = a^m+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