Question

Simplify:

`3^(2n - 1) xx 9^(1 - n)` 

Answer 1

Given,

`3^(2n - 1) xx 9^(1 - n)`

We have to simplify the given expression.

Thus, `3^(2n - 1) xx 9^(1 - n)`

⇒ `3^(2n - 1) xx (3^2)^(1 - n)`

⇒ `3^(2n - 1) xx (3)^(2(1 - n))`

⇒ `3^(2n - 1) xx (3)^((2 - 2n))`

⇒ `3^(2n - 1 + 2 - 2n)`  ...[∴ aⁿ × a^m = a^{n + m}]

⇒ 3¹ = 3

Hence, `3^(2n - 1) xx 9^(1 - n) = 3`