Задача

[Гост]

IMG-175e778edf5595eb62db6fded3e380ec-V.jpg (29.09 KiB) Прегледано 478 пъти

или

[ammornil]

[tex]a=-\frac{1}{2}, \hspace{1.5em} b=(-2)^{8}=2^{8}[/tex]

[tex]A=\left(\frac{2a^{3}}{3b^{2}} \right)^{4} \div \left(\frac{4a^{2}}{9b^{3}} \right)^{3}=\frac{(2a^{3})^{4}}{(3b^{2})^{4}} \cdot \frac{(3^{2}b^{3})^{3}}{(2^{2}a^{2})^{3}}=\frac{2^{1\cdot{4}}\cdot{a^{3\cdot{4}}}\cdot{3^{2\cdot{3}}}\cdot{b^{3\cdot{3}}}}{3^{1\cdot{4}}\cdot{b^{2\cdot{4}}}\cdot{2^{2\cdot{3}}}\cdot{a^{2\cdot{3}}}}=\frac{2^{4}\cdot{3^{6}}\cdot{a^{12}}\cdot{b^{9}}}{2^{6}\cdot{3^{4}}\cdot{a^{6}}\cdot{b^{8}}} \Rightarrow[/tex]

[tex]A=\frac{3^{2}\cdot{a^{6}}\cdot{b}}{2^{2}}=\frac{3^{2}\cdot{b}}{2^{2}}\cdot{a^{6}}=\frac{3^{2}\cdot{2^{8}}}{2^{2}}\cdot{\left(-\frac{1}{2} \right)^{6}}=\frac{3^{2}\cdot{2^{8}\cdot{1^{6}}}}{2^{2}\cdot{2^{6}}}=3^{2}=9[/tex]