Simplify the following:
$ \frac{3^n \times 9^{n+1}}{3^{n-1} \times 9^{n-1}} $

Given:

\( \frac{3 n \times 9^{n+1}}{3^{n-1} \times 9^{n-1}} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$  

$\frac{3^n \times 9^{n+1}}{3^{n-1} \times 9^{n-1}}=\frac{3^{n} \times(3^{2})^{n+1}}{3^{n-1} \times(3^{2})^{n-1}}$

$=\frac{3^{n} \times 3^{2 n+2}}{3^{n-1} \times 3^{2 n-2}}$

$=3^{2 n+2+n-n+1-2 n+2}$

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

$=3^{5}$

$=243$

Therefore, $\frac{3 n \times 9^{n+1}}{3^{n-1} \times 9^{n-1}}=243$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

38 Views

Kickstart Your Career

Get certified by completing the course

Get Started