Упростите выражение: $20a^5 \cdot (5a)^2$

1) а) $20a^5 \cdot (5a)^2 = 20a^5 \cdot 25a^2 = (20 \cdot 25) \cdot (a^5 \cdot a^2) = 500a^{5+2} = 500a^7$ б) $-0,4x^5 \cdot (2x^3)^4 = -0,4x^5 \cdot 2^4 \cdot (x^3)^4 = -0,4x^5 \cdot 16x^{3 \cdot 4} = -0,4x^5 \cdot 16x^{12} = (-0,4 \cdot 16) \cdot (x^5 \cdot x^{12}) = -6,4x^{5+12} = -6,4x^{17}$ в) $(-c^3)^2 \cdot 12c^6 = c^{3 \cdot 2} \cdot 12c^6 = c^6 \cdot 12c^6 = 12c^{6+6} = 12c^{12}$ 2) а) $(3x^2y^2)^4 \cdot \left(-\frac{1}{81}xy^2\right)^2 = 3^4(x^2)^4(y^2)^4 \cdot \left(-\frac{1}{81}\right)^2 x^2 (y^2)^2 = 81x^8y^8 \cdot \frac{1}{6561} x^2y^4 = \frac{81}{6561} x^{8+2}y^{8+4} = \frac{1}{81} x^{10}y^{12}$ б) $\left(-\frac{2}{3}ab^5\right)^3 \cdot 18a^9b = \left(-\frac{2}{3}\right)^3 a^3 (b^5)^3 \cdot 18a^9b = -\frac{8}{27} a^3b^{15} \cdot 18a^9b = \left(-\frac{8}{27} \cdot 18\right) (a^3 \cdot a^9) (b^{15} \cdot b) = \left(-\frac{8 \cdot 18}{27}\right) a^{3+9} b^{15+1} = -\frac{144}{27} a^{12}b^{16} = -\frac{16}{3} a^{12}b^{16}$ 7. Представьте в виде одночлена стандартного вида: 1) а) $(4ac^2)^3 \cdot (0,5a^3c)^2 = 4^3a^3(c^2)^3 \cdot (0,5)^2(a^3)^2c^2 = 64a^3c^6 \cdot 0,25a^6c^2 = (64 \cdot 0,25) (a^3 \cdot a^6) (c^6 \cdot c^2) = 16a^{3+6}c^{6+2} = 16a^9c^8$ б) $\left(\frac{2}{3}x^2y^3\right)^2 \cdot (-9x^4)^2 = \left(\frac{2}{3}\right)^2 (x^2)^2 (y^3)^2 \cdot (-9)^2 (x^4)^2 = \frac{4}{9}x^4y^6 \cdot 81x^8 = \left(\frac{4}{9} \cdot 81\right) (x^4 \cdot x^8) y^6 = 36x^{4+8}y^6 = 36x^{12}y^6$ 2) а) $-(-x^2y^4)^3 \cdot (6x^4y)^2 = -(-1)^3(x^2)^3(y^4)^3 \cdot 6^2(x^4)^2y^2 = -(-1)x^6y^{12} \cdot 36x^8y^2 = x^6y^{12} \cdot 36x^8y^2 = 36(x^6 \cdot x^8)(y^{12} \cdot y^2) = 36x^{6+8}y^{12+2} = 36x^{14}y^{14}$ б) $(-10a^3b^7)^3 \cdot (-0,2ab^2)^3 = (-10)^3(a^3)^3(b^7)^3 \cdot (-0,2)^3a^3(b^2)^3 = -1000a^9b^{21} \cdot (-0,008)a^3b^6 = (-1000 \cdot -0,008) (a^9 \cdot a^3) (b^{21} \cdot b^6) = 8a^{9+3}b^{21+6} = 8a^{12}b^{27}$