Упростите выражение:

1) a)$$14a^3 \cdot (5a)^4 = 14a^3 \cdot 5^4a^4 = 14a^3 \cdot 625a^4 = 14 \cdot 625 \cdot a^3 \cdot a^4 = 8750a^{3+4} = 8750a^7$$

1) б) $$-0,5b^2 \cdot (3b^2)^4 = -0,5b^2 \cdot 3^4(b^2)^4 = -0,5b^2 \cdot 81b^8 = -0,5 \cdot 81 \cdot b^2 \cdot b^8 = -40,5b^{2+8} = -40,5b^{10}$$

1) в) $$(-c^3)^3 \cdot 19c^3 = (-1)^3(c^3)^3 \cdot 19c^3 = -1 \cdot c^9 \cdot 19c^3 = -19c^{9+3} = -19c^{12}$$

2) a) $$(6d^3e^2)^4 \cdot (-\frac{1}{1296}de^3) = 6^4(d^3)^4(e^2)^4 \cdot (-\frac{1}{1296}de^3) = 1296d^{12}e^8 \cdot (-\frac{1}{1296}de^3) = 1296 \cdot (-\frac{1}{1296}) \cdot d^{12} \cdot d \cdot e^8 \cdot e^3 = -d^{12+1}e^{8+3} = -d^{13}e^{11}$$

2) б) $$(-\frac{1}{7}ef^2)^2 \cdot 21e^2f = (-\frac{1}{7})^2e^2(f^2)^2 \cdot 21e^2f = \frac{1}{49}e^2f^4 \cdot 21e^2f = \frac{1}{49} \cdot 21 \cdot e^2 \cdot e^2 \cdot f^4 \cdot f = \frac{21}{49}e^{2+2}f^{4+1} = \frac{3}{7}e^4f^5$$