Question

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

Answer 1

Answer:

$3^{2-n}$

Step-by-step explanation:

Given expression in the picture is,

$\frac{3^n}{9^{n-1}}$

= $\frac{3^n}{(3^2)^{n-1}}$

= $\frac{3^n}{3^{2(n-1)}}$

= $3^n\times 3^{-2(n-1)}$ [Since, $\frac{a^n}{a^m}=a^n\times a^{-m}$]

= $3^{n-2(n-1)}$ [Since, $a^m\times a^n=a^{m+n}$]

= $3^{n-2n+2}$

= $3^{2-n}$

Therefore, answer is $3^{2-n}$.