If {9^{ {n}} \times 3^{3} \times(27)^{3}}/{3 \times(81)^{4}}=243, then the value of n is

None of the above/More than one of the above

BPSC 65th Re Prelims Exam 17 Feb 2020 Solved Paper

Question : 145 of 150

Marks: +1, -0

\;{9^{ {n}} × 3^{3} ×(27)^{3}}/{3 ×(81)^{4}}=243,

then the value of

n

Solution:

\;{9^{ {n}} × 3^{5} ×(27)^{3}}/{3 ×(81)^{4}}=243

⇒ \;{9^{ {n}} ×(3)^{5} ×(3^{3})^{3}}/{3 ×(3^{4})^{4}}=(3)^{5}

⇒(3^{2})^{n} ×(3)^{5} ×(3)^{9}=(3)^{5} × 3^{1} ×(3)^{16}

⇒(3)^{2 n+14}=(3)^{22}

Since base is same,
so

2 n+14=22

⇒ n=\;{8}/{2}=4

Go to Question:

Prev Question

Next Question