If \frac{9^n \times 3^5 \times (27)^3}{3 \times (81)^4} = 27, then … — WBCS Main Examination 2023 Q43

Q43

ArithmeticAlgebra, Equations & Operations

If $\frac{9^n \times 3^5 \times (27)^3}{3 \times (81)^4} = 27$, then value of $n$ is

Answer: (C) 3

Writing everything as powers of 3, the left side is $\frac{3^{2n} \times 3^5 \times 3^9}{3^1 \times 3^{16}} = 3^{2n - 3}$. Setting $3^{2n - 3} = 3^3$ gives $2n = 6$, so $n = 3$. The other values give $3^{-3}$, $3^1$ or $3^5$.

WBCS Main Examination 2023 — Paper VI: Arithmetic and Test of Reasoning · Question 43 of 200