Question

Without calculating, find the value of the expression below. (7/8)^7 / (8/7)^8

Answer 1

1/56.

Explanation:

(7/8)^7 / (8/7)^8

= 7^7/8^7 / 8^8/7^8

= 7^7 / 8^7 * 7*8 / 8^8

= 7^(7-8) * 8^(7-8)

= 7^-1 * 8^-1

= 1/7 * 1/8

= 1/56.