Упр.155 ГДЗ Мерзляк Полонский 8 класс (Алгебра)
1) (4a2/b3) * x = 6a/b2;
2) (2b4/3c)3 : x = b6/12. Упростите выражение:
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.
$$\left(\frac{4a^2}{b^3}\right)^2 \cdot x=\frac{6a}{b^2}$$
$$x=\frac{6a}{b^2}:\left(\frac{4a^2}{b^3}\right)^2=\frac{6a}{b^2}:\frac{16a^4}{b^6}=\frac{6a\cdot b^6}{b^2\cdot 16a^4}=\frac{3b^4}{8a^3}$$
$$\left(\frac{2b^4}{3c}\right)^3:x=\frac{b^6}{12}$$
$$x=\left(\frac{2b^4}{3c}\right)^3:\frac{b^6}{12}=\frac{8b^{12}}{27c^3}\cdot\frac{12}{b^6}=\frac{32b^6}{9c^3}$$
$$\frac{6a^4b^2}{35c^3}\cdot\frac{14b^2}{a^7c^5}\cdot\frac{5a^3c^8}{18b^4}$$
$$=\frac{6\cdot 14\cdot 5\cdot a^4b^2\cdot b^2\cdot a^3c^8}{35\cdot 18\cdot c^3\cdot a^7c^5\cdot b^4}=\frac{2}{3}$$
$$\frac{33m^8}{34n^8}:\frac{88m^4}{51n^4}:\frac{21m^6}{16n^2}$$
$$=\frac{33m^8}{34n^8}\cdot\frac{51n^4}{88m^4}\cdot\frac{16n^2}{21m^6}=\frac{3}{7m^2n^2}$$
$$\frac{36x^6}{49y^5}:\frac{24x^9}{25y^4}\cdot\frac{7x^2}{30y}$$
$$=\frac{36x^6}{49y^5}\cdot\frac{25y^4}{24x^9}\cdot\frac{7x^2}{30y}=\frac{5}{28xy^2}$$
$$\left(\frac{m^5n}{3p^2}\right)^3:\frac{m^{10}n^5}{54p^8}$$
$$=\frac{m^{15}n^3}{27p^6}\cdot\frac{54p^8}{m^{10}n^5}=\frac{2m^5p^2}{n^2}$$
$$\left(\frac{2a^5}{y^6}\right)^4:\left(\frac{4a^6}{y^8}\right)^3$$
$$=\frac{16a^{20}}{y^{24}}:\frac{64a^{18}}{y^{24}}=\frac{16a^{20}}{y^{24}}\cdot\frac{y^{24}}{64a^{18}}=\frac{a^2}{4}$$
$$\left(-\frac{27x^3}{16y^5}\right)^2\cdot\left(\frac{8y^3}{9x^2}\right)^3$$
$$=\frac{27^2x^6}{16^2y^{10}}\cdot\frac{8^3y^9}{9^3x^6}=\frac{3^6x^6\cdot 2^9y^9}{2^8y^{10}\cdot 3^6x^6}=\frac{2}{y}$$
Ответ
1) $$\frac{3b^4}{8a^3}$$; 2) $$\frac{32b^6}{9c^3}$$; 3) $$\frac{2}{3}$$; 4) $$\frac{3}{7m^2n^2}$$; 5) $$\frac{5}{28xy^2}$$; 6) $$\frac{2m^5p^2}{n^2}$$; 7) $$\frac{a^2}{4}$$; 8) $$\frac{2}{y}$$.
