\(5^{(n-2)} \times 3^{(2 n-3)}=135\)
Simplifing,
\(\therefore 5^{(n)} \times 5^{(-2)} \times 3^{(2 n)} \times 3^{(-3)}=135\)
\(\therefore \frac{5^{n}}{5^{2}} \times \frac{3^{2 n}}{3^{3}}=135\)
\(\therefore \frac{5^{n}}{25} \times \frac{3^{2 n}}{27}=135\)
\(\therefore \frac{5^{n} \times 3^{2 n}}{675}=135\)
\(\therefore 5^{n} \times 3^{2 n}=135 \times 675\)
\(\therefore 5^{n} \times 3^{2 n}=91125\)
\(\therefore 5^{n} \times 3^{2 n}=5 \times 5 \times 5 \times 9 \times 9 \times 9\)
\(\therefore 5^{n} \times 9^{n}=5^{3} \times 9^{3} \quad\left(\because 3^{2 n}=9^{n}\right)\)
Comparing both sides, we get the value of n as 3.
