Question

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

Answer 1

2160 = 2^a x 3^b x 5^c
⇒ 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 = 2^a x 3^b x 5^c
⇒ 2⁴ x 3³ x 5¹ = 2^a x 3^b x 5^c
⇒ 2^a x 3^b x 5^c = 2⁴ x 3³ x 5¹
Comparing powers of 2, 3 and 5 on the both sides of equation, We have
a = 4; b = 3 and c = 1
Hence,
Value of 3^a x 2^-b x 5^-c
= 3⁴ x 2^-3 x 5^-1
= 3 x 3 x 3 x 3 x `1/2^3 xx 1/5` 

= `81 xx 1/[ 2 xx 2 xx 2 ] xx 1/5`

= `81 xx 1/8 xx 1/5`

= `81/40`

= `2 1/40`