[9] \dfrac{243^{\dfrac{n}{5} \times} 3^{2n+1}}{9^{n} \times 3^{n-1}}=?

For Competitive Exams

$\dfrac{243^{\dfrac{n}{5} \times} 3^{2n+1}}{9^{n} \times 3^{n-1}}=?$

Explanation:

Given Expression $=\dfrac{243^{\dfrac{n}{5} \times} 3^{2n+1}}{9^{n} \times 3^{n-1}}$

$=\dfrac{\left(3^{5}\right)^{\dfrac{n}{5} }\times 3^{2n+1}}{\left(3^{2}\right)^{n} \times 3^{n-1}}$

$=\dfrac{3^{\left(5 \times \dfrac{n}{5} \right)} \times 3^{2n+1}}{3^{2n}\times 3^{n-1}}$

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

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

$=\dfrac{ 3^{3n+1}}{ 3^{3n-1}}$

$=3^{\left(3n+1-3n+1\right)}$

$=3^{2}=9$

Additional Questions

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