ABC26GN1878 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
Find the value of $\frac{(243)^{\frac{n}{5}} \cdot 3^{2 n+1}}{9^{n} \times 3^{n-1}}$.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
$\frac{(243)^{\frac{n}{5}} \cdot 3^{2 n+1}}{9^{n} \times 3^{n-1}}=\frac{\left(3^{5}\right)^{\frac{n}{5}} \times 3^{2 n+1}}{\left(3^{2}\right)^{n} \times 3^{n-1}}=\frac{3^{\left(5 \times \frac{n}{5}\right)} \times 3^{2 n+1}}{3^{2 n} \times 3^{n-1}}=\frac{3^{n} \times 3^{2 n+1}}{3^{2 n} \times 3^{n-1}}=\frac{3^{n+(2 n+1)}}{3^{2 n+n-1}}=\frac{3^{(3 n+1)}}{3^{(3 n-1)}}=3^{(3 n+1)-(3 n-1)}=3^{2}=9.$
Explanation as extracted from the printed page; notation may be imperfect.
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