a. \(\dfrac{5}{2}+\left(\dfrac{-3}{2}\right)^2.6-\left|-5\right|\)
\(=\dfrac{5}{2}+\dfrac{9}{4}.6-5\)
\(=\dfrac{5}{2}+\dfrac{27}{2}-5\)
\(=11\)
b. \(\dfrac{250^3}{50^3}=\left(\dfrac{250}{50}\right)^3=5^3=125\)
c. \(\dfrac{45^{10}.5^{20}}{75^{15}}=\dfrac{\left(5.3.3\right)^{10}.5^{20}}{\left(5.5.3\right)^{15}}=\dfrac{5^{10}.3^{10}.3^{10}.5^{20}}{5^{15}.5^{15}.3^{15}}=\dfrac{5^{30}.3^{20}}{5^{30}.3^{15}}=3^5=243\)