\( A = (\frac{2}{5})^3 \times (\frac{2}{5})^{-9} \)
\( A = (\frac{2}{5})^{3 + (-9)} \)
\( A = (\frac{2}{5})^{-6} \)
\( A = (\frac{5}{2})^6 \)
\( B = \frac{(-\frac{5}{7})^{10}}{(\frac{5}{7})^6} \)
بما أن دليل القوة 10 زوجي: \( (-\frac{5}{7})^{10} = (\frac{5}{7})^{10} \)
\( B = (\frac{5}{7})^{10 - 6} \)
\( B = (\frac{5}{7})^4 \)
\( C = \sqrt{\frac{625}{169}} + \sqrt{13 + 6^2} \)
\( C = \frac{\sqrt{625}}{\sqrt{169}} + \sqrt{13 + 36} \)
\( C = \frac{25}{13} + \sqrt{49} \)
\( C = \frac{25}{13} + 7 = \frac{25 + 91}{13} \)
\( C = \frac{116}{13} \)
\( D = \frac{(10^{-1})^2 \times 10^3}{(10^{-3})^{-2} \times 10^{-8}} \)
البسط: \( 10^{-2} \times 10^3 = 10^1 \)
المقام: \( 10^6 \times 10^{-8} = 10^{-2} \)
النتيجة: \( \frac{10^1}{10^{-2}} = 10^{1 - (-2)} = 10^3 = 1000 \)
\( E = \frac{x^6 (x^5 y^{-4})^2 y^3}{y^7 (x^4 y^5)^{-3} x^8} \)
\( E = \frac{x^6 \cdot x^{10} y^{-8} \cdot y^3}{y^7 \cdot x^{-12} y^{-15} \cdot x^8} \)
\( E = \frac{x^{16} y^{-5}}{x^{-4} y^{-8}} \)
\( E = x^{16 - (-4)} \cdot y^{-5 - (-8)} \)
\( E = x^{20} y^3 \)