[3] If \dfrac{9^{n} \times 3^{5} \times \left(27\right)^{3}}{3 \times \left(81\right)^{4}}=27, then th

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If $\dfrac{9^{n} \times 3^{5} \times \left(27\right)^{3}}{3 \times \left(81\right)^{4}}=27$, then the value of n is:

Explanation:

$\dfrac{9^{n} \times 3^{5} \times \left(27\right)^{3}}{3 \times \left(81\right)^{4}}=27$

$\Leftrightarrow \dfrac{\left(3^{2}\right)^{n} \times 3^{5} \times \left(3^{3}\right)^{3}}{3 \times \left(3\right)^{4\times 4}}=3^{3}$

$\Leftrightarrow \dfrac{\left(3\right)^{2n} \times 3^{5} \times \left(3\right)^{3\times 3}}{3 \times \left(3\right)^{4\times 4}}=3^{3}$

$\Leftrightarrow\dfrac{3^{2n+5+9}}{3 \times 3^{16}}=3^{3}$

$\Leftrightarrow\dfrac{3^{2n+14}}{ 3^{17}}=3^{3}$

$\Leftrightarrow 3^{\left(2n+14-17\right)}=3^{3}$

$\Leftrightarrow 3^{\left(2n-3\right)}=3^{3}$

$=2n-3 = 3 $

$\Leftrightarrow 2n=6$

$\Leftrightarrow n=3$

Additional Questions

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$\dfrac{(243)^{n/5} \times 3^{2n+1}}{9^{n}\times 3^{n-1}}$=?	Answer
(25)^7.5 x (5)^2.5 ÷ (125)^1.5 = 5^?	Answer
If x = 3 + 2$\sqrt{2}$, then the value of $\left( \sqrt{x} -\dfrac{1}{\sqrt{x}} \right)$ is:	Answer
$\dfrac{1}{1+x^{(b-a)}+x^{(c-a)}}+\dfrac{1}{1+x^{(a-b)}+x^{(c-b)}}+\dfrac{1}{1+x^{(b-c)}+x^{(a-c)}}$	Answer
Which is larget √2 or $\sqrt[3]{3}$?	Answer
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$\dfrac{243^{\dfrac{n}{5} \times} 3^{2n+1}}{9^{n} \times 3^{n-1}}=?$	Answer
If $\dfrac{9^{n} \times 3^{5} \times \left(27\right)^{3}}{3 \times \left(81\right)^{4}}=27$, then the value of n is:	Answer

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