Question

2160=2^a . 3^b . 5^c find a,b and c .Hence calculate the value of 3^a . 2^-b . 5^-c.

Answer 1

Answer:

a=4, b=3, c=1 ; 3^a.2^-b.5^-c=81/40 or 2.25

Step-by-step explanation:

we obtain the values of a, b, c by prime factorisation of 2160

2160=2 x 2 x 2 x 2 x 3 x 3 x 3 x 5

       = 2^4 x 3^3 x 5^1

on substituting the values of a, b, c in 3^a x 2^-b x 5^-c

we get

3^4 x 2^-3 x 5^-1 = 81/(8 x 5) = 81/40 or 2.25