Упростить: 5⁷·(5⁻³)²/(5⁴)²; 3⁴·27/(3²)⁶.

1. \(\frac{5^7\cdot(5^{-3})^2}{(5^4)^2}=\frac{5^7\cdot5^{-6}}{5^8}=5^{7-6-8}=5^{-7}=\frac1{78125}\).

2. Представим \(27=3^3\): \(\frac{3^4\cdot27}{(3^2)^6}=\frac{3^4\cdot3^3}{3^{12}}=3^{4+3-12}=3^{-5}=\frac1{243}\).

Ответ: 1/78125; 1/243.