6. Упростите выражение: 1) a) 20a³ (5a)²; б) -0,4x5. (2х3)4; в) (-с³)212c6; 2) a) (3x6y3). (-xy²); 6) (-abs) 18ab.

6. Упростите выражение:

1) a) $$20a^3 \cdot (5a)^2 = 20a^3 \cdot 5^2 \cdot a^2 = 20a^3 \cdot 25a^2 = 20 \cdot 25 \cdot a^3 \cdot a^2 = 500a^{3+2} = 500a^5$$

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) $$(-c^3)^2 \cdot 12c^6 = (-1)^2 \cdot (c^3)^2 \cdot 12c^6 = 1 \cdot c^{3 \cdot 2} \cdot 12c^6 = c^6 \cdot 12c^6 = 12 \cdot c^6 \cdot c^6 = 12c^{6+6} = 12c^{12}$$

2) a) $$(3x^6y^3)^4 \cdot \left(-\frac{1}{81}xy^2\right) = 3^4 \cdot (x^6)^4 \cdot (y^3)^4 \cdot \left(-\frac{1}{81}xy^2\right) = 81x^{6 \cdot 4}y^{3 \cdot 4} \cdot \left(-\frac{1}{81}xy^2\right) = 81x^{24}y^{12} \cdot \left(-\frac{1}{81}xy^2\right) = 81 \cdot \left(-\frac{1}{81}\right) \cdot x^{24} \cdot x \cdot y^{12} \cdot y^2 = -x^{24+1}y^{12+2} = -x^{25}y^{14}$$

б) $$\left(-\frac{2}{3}ab^5\right) \cdot 18a^5b = -\frac{2}{3} \cdot 18 \cdot a \cdot a^5 \cdot b^5 \cdot b = -\frac{2 \cdot 18}{3} \cdot a^{1+5}b^{5+1} = -\frac{36}{3}a^6b^6 = -12a^6b^6$$

Ответ: 1) а) $$500a^5$$, б) $$-6,4x^{17}$$, в) $$12c^{12}$$ 2) а) $$-x^{25}y^{14}$$, б) $$-12a^6b^6$$