Решение:

1. a) $$(0.3x)^3 = 0.3^3 \cdot x^3 = 0.027x^3$$
2. б) $$(-6x^4y)^2 = (-6)^2 \cdot (x^4)^2 \cdot y^2 = 36x^8y^2$$
3. в) $$\left(\frac{3}{5}mn^3\right)^4 = \left(\frac{3}{5}\right)^4 \cdot m^4 \cdot (n^3)^4 = \frac{81}{625}m^4n^{12}$$
4. г) $$\left(1\frac{2}{3}p^3q^7\right)^3 = \left(\frac{5}{3}\right)^3 \cdot (p^3)^3 \cdot (q^7)^3 = \frac{125}{27}p^9q^{21}$$
5. д) $$(-2a^6b^3)^6 = (-2)^6 \cdot (a^6)^6 \cdot (b^3)^6 = 64a^{36}b^{18}$$