Question

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

Answer 1

1960 = 2^a × 5^b × 7^c

⇒ 2 × 2 × 2 × 5 × 7 × 7 = 2^{a ×} 5^{b ×} 7^c

⇒ 2³ × 5¹ × 7² = 2^a × 5^b × 7^c

⇒  2^a × 5^b × 7^c = 2³ × 5¹ × 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 × 7^b × 5^-c 

= 2^-3 × 7¹ × 5^-2

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

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

= `7/200`