Упр.1080 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (a5/x4)2;
2) (-4y/3m2)4;
3) (-10x2y5/3a4b3)3;
4) (-2a4b4/25×5) * (-5×2/4a2b3)3.

1. $$\left(\frac{a^5}{x^4}\right)^2=\frac{(a^5)^2}{(x^4)^2}=\frac{a^{10}}{x^8}.$$

2. $$\left(-\frac{4y}{3m^2}\right)^4=\frac{(-4y)^4}{(3m^2)^4}=\frac{4^4y^4}{3^4m^8}=\frac{256y^4}{81m^8}.$$

3. $$\left(-\frac{10x^2y^5}{3a^4b^3}\right)^3=-\frac{10^3x^6y^{15}}{3^3a^{12}b^9}=-\frac{1000x^6y^{15}}{27a^{12}b^9}.$$

4. $$\left(-\frac{2a^4b^4}{25x^5}\right)^2\cdot\left(-\frac{5x^2}{4a^2b^3}\right)^3$$
   $$=\frac{2^2a^8b^8}{25^2x^{10}}\cdot\left(-\frac{5^3x^6}{4^3a^6b^9}\right)$$
   $$=-\frac{2^2\cdot 5^3a^8b^8x^6}{(5^2)^2\cdot(2^2)^3x^{10}a^6b^9}$$
   $$=-\frac{2^2\cdot 5^3a^2}{5^4\cdot 2^6x^4b}=-\frac{a^2}{80x^4b}.$$

Ответ

$$\frac{a^{10}}{x^8};\ \frac{256y^4}{81m^8};\ -\frac{1000x^6y^{15}}{27a^{12}b^9};\ -\frac{a^2}{80x^4b}.$$