8. Упростите выражение: 1) \(a^4\cdot(a^4)^3\); 2) \(\frac{(x^3)^6\cdot x^4}{x^{18}}\); 3) \(x^3\cdot(x^3)^4\); 4) \(\frac{(x^4)\cdot x^2}{x^{12}}\).

1. \(a^4\cdot(a^4)^3=a^4\cdot a^{12}=a^{16}\).
2. \(\frac{(x^3)^6\cdot x^4}{x^{18}}=\frac{x^{18}\cdot x^4}{x^{18}}=x^4\), \(x\ne0\).
3. \(x^3\cdot(x^3)^4=x^3\cdot x^{12}=x^{15}\).
4. \(\frac{(x^4)\cdot x^2}{x^{12}}=\frac{x^6}{x^{12}}=\frac1{x^6}\), \(x\ne0\).

Ответ: 1) \(a^{16}\); 2) \(x^4\); 3) \(x^{15}\); 4) \(\frac1{x^6}\).