Упр.153 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) 6a4b2/35c3 * 14b2/a7c5 * 5a3c8/18b4;
2) 33m8/34n8 : 88m4/51n4 : 21m6/16n2;
3) 36×6/49y5 : 24×9/25y4 * 7×2/30y;
4) (m5n/3p2)3 : m10n5/54p8;
5) (2a5/y6)4 : (4a6/y8)3;
6) (-27×3/16y5)2 * (8y3/9×2)3. Выполните возведение в степень:
1) (a/b)9;
2) (m/n2)8;
3) (c/2d)5;
4) (5a6/b5)2;
5) (-3m4/2n3)3;
6) (-6a6/b7)2.

1. $$\frac{6a^4b^2}{35c^3}\cdot\frac{14b^2}{a^7c^5}\cdot\frac{5a^3c^8}{18b^4}=
   \frac{6\cdot14\cdot5\cdot a^{4+3}b^{2+2}c^8}{35\cdot18\cdot a^7c^{3+5}b^4}=
   \frac{6\cdot14\cdot5}{35\cdot18}\cdot\frac{a^7}{a^7}\cdot\frac{b^4}{b^4}\cdot\frac{c^8}{c^8}=
   \frac{2}{3}$$
2. $$\frac{33m^8}{34n^8}:\frac{88m^4}{51n^4}:\frac{21m^6}{16n^2}=
   \frac{33m^8}{34n^8}\cdot\frac{51n^4}{88m^4}\cdot\frac{16n^2}{21m^6}$$
   $$=
   \frac{33\cdot51\cdot16}{34\cdot88\cdot21}\cdot\frac{m^8}{m^{4+6}}\cdot\frac{n^{4+2}}{n^8}
   =
   \frac{3}{7m^2n^2}$$
3. $$\frac{36x^6}{49y^5}:\frac{24x^9}{25y^4}\cdot\frac{7x^2}{30y}=
   \frac{36x^6}{49y^5}\cdot\frac{25y^4}{24x^9}\cdot\frac{7x^2}{30y}$$
   $$=
   \frac{36\cdot25\cdot7}{49\cdot24\cdot30}\cdot\frac{x^{6+2}}{x^9}\cdot\frac{y^4}{y^{5+1}}
   =
   \frac{5}{28xy^2}$$
4. $$\left(\frac{m^5n}{3p^2}\right)^3:\frac{m^{10}n^5}{54p^8}
   =
   \frac{m^{15}n^3}{27p^6}\cdot\frac{54p^8}{m^{10}n^5}$$
   $$=
   \frac{54}{27}\cdot m^{15-10}\cdot n^{3-5}\cdot p^{8-6}
   =
   \frac{2m^5p^2}{n^2}$$
5. $$\left(\frac{2a^5}{y^6}\right)^4:\left(\frac{4a^6}{y^8}\right)^3
   =
   \frac{16a^{20}}{y^{24}}:\frac{64a^{18}}{y^{24}}
   =
   \frac{16a^{20}}{y^{24}}\cdot\frac{y^{24}}{64a^{18}}$$
   $$=
   \frac{16}{64}\cdot a^{20-18}
   =
   \frac{a^2}{4}$$
6. $$\left(-\frac{27x^3}{16y^5}\right)^2\cdot\left(\frac{8y^3}{9x^2}\right)^3
   =
   \frac{27^2x^6}{16^2y^{10}}\cdot\frac{8^3y^9}{9^3x^6}$$
   $$=
   \frac{27^2\cdot8^3}{16^2\cdot9^3}\cdot\frac{y^9}{y^{10}}
   =
   \frac{3}{2y}$$

Ответ

1. $$\frac{2}{3}$$
2. $$\frac{3}{7m^2n^2}$$
3. $$\frac{5}{28xy^2}$$
4. $$\frac{2m^5p^2}{n^2}$$
5. $$\frac{a^2}{4}$$
6. $$\frac{3}{2y}$$

Возведение в степень:

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. $$\left(\frac{c}{2d}\right)^5=\frac{c^5}{32d^5}$$
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. $$\left(-\frac{6a^6}{b^7}\right)^2=\frac{36a^{12}}{b^{14}}$$