Question

Simplify:

`(x^a)^(b - c) (x^b)^(c - a) (x^c)^(a - b)`

Answer 1

Given,

`(x^a)^(b - c) (x^b)^(c - a) (x^c)^(a - b)`

We need to simplify.

Thus, `(x^a)^(b - c) (x^b)^(c - a) (x^c)^(a - b)`

⇒ `(x)^(a(b - c)) xx (x)^(b(c - a)) xx (x)^(c(a - b))`  ...[∵ (aⁿ)^m = a^nm]

⇒ `(x)^(ab - ac) xx (x)^(bc - ba) xx (x)^(ca - cb)`

⇒ `(x)^(ab - ac + bc - ba + ca - cb)`   ...[∵ aⁿ × a^m = a^{n + m}]

⇒ (x)⁰ = 1

Hence, the required is 1.