Question

If 2250 = 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

Given 2250 = 2^a · 3^b · 5^c
⇒ 3² x 5³ x 2 = 2^a · 3^b · 5
⇒ a = 1, b = 2, c = 3
3^a x 2^-b x 5^-x
= 3¹ x 2^-2 x 5^-3

= `(3)/(2^2 xx 5^3)`

= `(3)/(500)`.