\( A = \left(\frac{3}{5}\right)^{-12} \times \left(\frac{3}{5}\right)^{18} \)
\( = \left(\frac{3}{5}\right)^{-12 + 18} \)
\( = \left(\frac{3}{5}\right)^{6} \)
\( B = \frac{(-11/3)^9}{(-5/2)^9} \)
\( = \left( \frac{-11/3}{-5/2} \right)^9 \)
\( = \left( \frac{11}{3} \times \frac{2}{5} \right)^9 \)
\( = \left( \frac{22}{15} \right)^9 \)
\( K = \left[ \left(\frac{2}{3}\right)^{-4} \right]^5 \times \frac{16}{81} \)
\( = \left(\frac{2}{3}\right)^{-20} \times \left(\frac{2}{3}\right)^4 \)
\( = \left(\frac{2}{3}\right)^{-20 + 4} \)
\( = \left(\frac{2}{3}\right)^{-16} = \left(\frac{3}{2}\right)^{16} \)
\( \frac{0,001^4 \times 1000^{-2}}{100^{-3} \times 0,01^{-5}} \)
\( = \frac{(10^{-3})^4 \times (10^3)^{-2}}{(10^2)^{-3} \times (10^{-2})^{-5}} \)
\( = \frac{10^{-12} \times 10^{-6}}{10^{-6} \times 10^{10}} \)
\( = \frac{10^{-18}}{10^4} = 10^{-22} \)
\( \frac{x^6 (x^5 y^{-4})^2 y^3}{y^7 (x^4 y^5)^{-3} x^8} \)
\( = \frac{x^6 \cdot x^{10} y^{-8} \cdot y^3}{y^7 \cdot x^{-12} y^{-15} \cdot x^8} \)
\( = \frac{x^{16} y^{-5}}{x^{-4} y^{-8}} \)
\( = x^{16 - (-4)} \cdot y^{-5 - (-8)} \)
\( = x^{20} y^3 \)
\( \frac{(x^{-4} y^{-3})^2}{(x^3 y^2)^{-3}} \)
\( = \frac{x^{-8} y^{-6}}{x^{-9} y^{-6}} \)
\( = x^{-8 - (-9)} \cdot y^{-6 - (-6)} \)
\( = x^1 \cdot y^0 = x \)
\( B = \frac{\sqrt{4/9} - 3 \times \sqrt{25}/6}{3/2 \times \sqrt{50/72} - 9/4} \)
البسط: \( \frac{2}{3} - 3 \times \frac{5}{6} = \frac{2}{3} - \frac{5}{2} = -\frac{11}{6} \)
المقام: \( \frac{3}{2} \times \sqrt{25/36} - \frac{9}{4} = \frac{3}{2} \times \frac{5}{6} - \frac{9}{4} \)
النتيجة: \( B = \frac{-11/6}{-1} = \frac{11}{6} \)
\( f = \sqrt{9^2 + 19} + \sqrt{\frac{25}{4}} \)
\( = \sqrt{81 + 19} + \frac{5}{2} \)
\( = \sqrt{100} + 2,5 = 10 + 2,5 \)
\( = 12,5 \)