Question

If 1960 = 2^a. 5^b. 7^c, calculate the value of 2^-a. 7^b. 5^-c.

Answer 1

1960 = 2^a x 5^b x 7^c
⇒ 2 x 2 x 2 x 5 x 7 x 7 = 2^a x 5^b x 7^c
⇒ 2³ x 5¹ x 7² = 2^a x 5^b x 7^c
⇒  2^ax 5^b x 7^c = 2³ x 5¹ x 7²
Comparing powers of 2,5 and 7 on the both sides of equation, We have
a = 3; b = 1 and c = 2
Hence,
Value of 2^-a x 7^b x 5^-c

= 2^-3 x 7¹ x 5^-2

= `1/2^3 xx 7 xx 1/5^2`

= `1/8 xx 7 xx 1/[ 5 xx 5 ]`

= `7/200`