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