Question

Write [equation in the the picture as a power of 3] the powers are n

Answer 1

`3^(2-n)`

Explanation:

Given expression in the picture is,

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

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

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

=
`3^n* 3^(-2(n-1))` [Since,
`(a^n)/(a^m)=a^n* a^(-m)`]

=
`3^(n-2(n-1))` [Since,
`a^m* a^n=a^(m+n)`]

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

=
`3^(2-n)`

Therefore, answer is
`3^(2-n)`.