Упражнение 155

\(1)\ \frac{6a^4b^2}{35c^3}\cdot\frac{14b^2}{a^7c^5}\cdot\frac{5a^3c^8}{18b^4}=\frac{6a^4b^2\cdot14b^2\cdot5a^3c^8}{35c^3\cdot{a}^7c^5\cdot18b^4}=\frac{6\cdot14\cdot5\cdot{a}^7b^4c^8}{35\cdot18\cdot{a}^7b^4c^8}=\frac{2}{3};\)

\(2)\ \frac{33m^8}{34n^8}:\frac{88m^4}{51n^4}:\frac{21m^6}{16n^2}=\frac{33m^8}{34n^8}\cdot\frac{51n^4}{88m^4}\cdot\frac{16n^2}{21m^6}=\frac{33m^8\cdot51n^4\cdot16n^2}{34n^8\cdot88m^4\cdot21m^6}=\frac{33\cdot51\cdot16\cdot{m}^8n^6}{34\cdot88\cdot21\cdot{m}^{10}n^8}=\frac{3}{7m^2n^2};\)

\(3)\ \frac{36x^6}{49y^5}:\frac{24x^9}{25y^4}\cdot\frac{7x^2}{30y}=\frac{36x^6}{49y^5}\cdot\frac{25y^4}{24x^9}\cdot\frac{7x^2}{30y}=\frac{36x^6\cdot25y^4\cdot7x^2}{49y^5\cdot24x^9\cdot30y}=\frac{36\cdot25\cdot7\cdot{x}^8y^4}{49\cdot24\cdot30\cdot{x}^9y^6}=\frac{5}{28xy^2};\)

\(4)\ \left(\frac{m^5n}{3p^3}\right)^3:\frac{m^{10}n^5}{54p^8}=\left(\frac{m^5n}{3p^3}\right)^3\cdot\frac{54p^8}{m^{10}n^5}=\frac{ (m^5n)^3}{ (3p^3)^3}\cdot\frac{54p^8}{m^{10}n^5}=\frac{m^{15}n^3}{27p^9}\cdot\frac{54p^8}{m^{10}n^5}=\frac{m^{15}n^3\cdot54p^8}{27p^9\cdot{m}^{10}n^5}=\frac{2m^5}{n^2p};\)

\(5)\ \left(\frac{2a^5}{y^6}\right)^4:\left(\frac{4a^6}{y^8}\right)^3=\left(\frac{2a^5}{y^6}\right)^4\cdot\left(\frac{y^8}{4a^6}\right)^3=\frac{ (2a^5)^4}{ (y^6)^4}\cdot\frac{ (y^8)^3}{ (4a^6)^3}=\frac{16a^{20}}{y^{24}}\cdot\frac{y^{24}}{64a^{18}}=\frac{16a^{20}\cdot{y}^{24}}{y^{24}\cdot64a^{18}}=\frac{a^2}{4};\)

\(6)\ \left({-}\frac{27x^3}{16y^5}\right)^2\cdot\left(\frac{8y^3}{9x^2}\right)^3=\frac{ (3^3x^3)^2}{ (2^4y^5)^2}\cdot\frac{ (2^3y^3)^3}{ (3^2x^2)^3}=\frac{3^6x^6}{2^8y^{10}}\cdot\frac{2^9y^9}{3^6x^6}=\frac{3^6x^6\cdot2^9y^9}{2^8y^{10}\cdot3^6x^6}=\frac{2}{y}.\)