Express each of the following numbers as a product of powers of their

1.	Express each of the following numbers as a product of powers of their prime factors:(i) 450(ii) 2800(iii) 24000
Answer» (i) Given 450 Prime factorization of 450 = 2 x 3 x 3 x 5 x 5 = 2 x 3² x 5² (ii) Given 2800 Prime factorization of 2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7 = 2⁴ x 5² x 7 (iii) Given 24000 Prime factorization 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

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

Answer»

(i) Given 450

Prime factorization of 450 = 2 x 3 x 3 x 5 x 5

= 2 x 3² x 5²

(ii) Given 2800

Prime factorization of 2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7

= 2⁴ x 5² x 7

(iii) Given 24000

Prime factorization 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