Question

`((-1)/4)^3 xx ((-1)/4)^- = ((-1)/4)^11`

Answer 1

`((-1)/4)^3 xx ((-1)/4)^bb(underline(8)) = ((-1)/4)^11`

Explanation:

Let `((-1)/4)^3 xx ((-1)/4)^x = ((-1)/4)^11`

⇒ `((-1)/4)^x = ((-1)/4)^11/((-1)/4)^3`

⇒ `((-1)/4)^x = ((-1)/4)^(11 - 3)`  ...[∵ a^m ÷ aⁿ = a^{m – n}, m > n]

⇒ `((-1)/4)^x = ((-1)/4)^8`

Since, base are equal.

So, by equating the powers, we get 

x = 8

∴ `((-1)/4)^3 xx ((-1)/4)^8 = ((-1)/4)^11`