Question

`(3^(n + 1) xx 9^(n - 1))/(3^n xx 9^(n + 1))` is equal to ______.

Options

• 27

• 9

• `1/9`

• `1/27`

Answer 1

`(3^(n + 1) xx 9^(n - 1))/(3^n xx 9^(n + 1))` is equal to `underlinebb(1/27)`.

Explanation:

The given expression is:

`(3^(n + 1) xx 9^(n - 1))/(3^n xx 9^(n + 1))`

First, express 9 as a power of 3:

9 = 3²

Substitute:

= `(3^(n + 1) xx (3^2)^(n - 1))/(3^n xx (3^2)^(n + 1))`

= `(3^(n + 1) xx 3^(2(n - 1)))/(3^n xx 3^(2(n + 1))`

Simplify powers of 3:

= `(3^(n + 1 + 2n - 2))/(3^(n + 2n + 2))`

= `(3^(3n - 1))/(3^(3n + 2))`

= `3^((3n - 1) - (3n + 2))`

= `3^-3`

= `1/3^3`

= `1/27`

So, the value of the expression is `1/27`.