Упр.151 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (a/b)9;
2) (m/n2)8;
3) (c/2d)5;
4) (5a6/b5)2;
5) (-3m4/2n3)3;
6) (-6a6/b7)2. Упростите выражение:
1) (a-b)/7a : (a-b)/7b;
2) (x2-y2)/x2 : (6x+6y)/x5;

1. $$\left(\frac{a}{b}\right)^9=\frac{a^9}{b^9}$$
2. $$\left(\frac{m}{n^2}\right)^8=\frac{m^8}{n^{16}}$$
3. $$\left(\frac{c}{2d}\right)^5=\frac{c^5}{2^5d^5}=\frac{c^5}{32d^5}$$
4. $$\left(\frac{5a^6}{b^5}\right)^2=\frac{25a^{12}}{b^{10}}$$
5. $$\left(-\frac{3m^4}{2n^3}\right)^3=-\frac{27m^{12}}{8n^9}$$
6. $$\left(-\frac{6a^6}{b^7}\right)^2=\frac{36a^{12}}{b^{14}}$$
7. $$\frac{a-b}{7a}:\frac{a-b}{7b}=\frac{a-b}{7a}\cdot\frac{7b}{a-b}=\frac{b}{a}$$
8. $$\frac{x^2-y^2}{x^2}:\frac{6x+6y}{x^5}=\frac{(x-y)(x+y)}{x^2}:\frac{6(x+y)}{x^5}$$
   $$=\frac{(x-y)(x+y)}{x^2}\cdot\frac{x^5}{6(x+y)}=\frac{x^3(x-y)}{6}$$

Ответ

1) $$\frac{a^9}{b^9}$$; 2) $$\frac{m^8}{n^{16}}$$; 3) $$\frac{c^5}{32d^5}$$; 4) $$\frac{25a^{12}}{b^{10}}$$; 5) $$-\frac{27m^{12}}{8n^9}$$; 6) $$\frac{36a^{12}}{b^{14}}$$; 7) $$\frac{b}{a}$$; 8) $$\frac{x^3(x-y)}{6}$$.