\( A = \sqrt{\frac{625}{169}} + \sqrt{13 + 6^2} \)
\( = \frac{\sqrt{625}}{\sqrt{169}} + \sqrt{13 + 36} \)
\( = \frac{25}{13} + \sqrt{49} \)
\( = \frac{25}{13} + 7 \)
\( = \frac{25}{13} + \frac{91}{13} = \frac{116}{13} \)
\( H = \frac{(x^2 y)^{-3} \cdot x^8 y^2}{(x y^2)^{-2}} \)
\( = \frac{x^{-6} y^{-3} \cdot x^8 y^2}{x^{-2} y^{-4}} \)
\( = \frac{x^{-6+8} \cdot y^{-3+2}}{x^{-2} y^{-4}} \)
\( = \frac{x^2 y^{-1}}{x^{-2} y^{-4}} \)
\( = x^{2 - (-2)} \cdot y^{-1 - (-4)} = x^4 y^3 \)
\( E = \frac{(3/4)^{-2} \times (3/4)^5}{[ (3/4)^2 ]^3} \times (4/3)^{-4} \)
\( = \frac{(3/4)^{3}}{(3/4)^6} \times (3/4)^4 \)
\( = (3/4)^{3-6} \times (3/4)^4 \)
\( = (3/4)^{-3} \times (3/4)^4 \)
\( = (3/4)^1 = \frac{3}{4} \)
\( \frac{(-19)^{167}}{(-19)^{57}} \times (-19)^{-100} \)
\( = (-19)^{167-57} \times (-19)^{-100} \)
\( = (-19)^{110} \times (-19)^{-100} \)
\( = (-19)^{110 - 100} = (-19)^{10} \)
بما أن 10 زوجي: \( = 19^{10} \)