Simplify the following:$ \frac{\left(a^{3 n-9}\right)^{6}}{a^{2 n-4}} $

Given:

\( \frac{\left(a^{3 n-9}\right)^{6}}{a^{2 n-4}} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

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

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

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

$a^{0}=1$  Therefore,

$\frac{(a^{3 n-9})^{6}}{a^{2 n-4}}=\frac{a^{(3 n-9) 6}}{a^{2 n-4}}$

$=\frac{a^{18 n-54}}{a^{2 n-4}}$

$=a^{(18 n-54-2 n+4)}$

$=a^{(16 n-50)}$

Hence, $\frac{(a^{3 n-9})^{6}}{a^{2 n-4}}=a^{(16 n-50)}$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

32 Views

Kickstart Your Career

Get certified by completing the course

Get Started