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解：?$(2)$?因?yàn)?$(\frac {5}{4})^3=\frac {5}{4}×\frac {5}{4}×\frac {5}{4}=\frac {125}{64}，$?
?$(\frac {4}{5})^{-3}=\frac {1}{(\frac {4}{5})^3}=\frac {1}{\frac {4}{5}×\frac {4}{5}×\frac {4}{5}}=\frac {5}{4}×\frac {5}{4}×\frac {5}{4}=\frac {125}{64}，$?
所以?$(\frac {5}{4})^3=(\frac {4}{5})^{-3}。$?
?$(4)①(\frac {3}{8})^{-4}=(\frac {8}{3})^4，$?
所以原式?$=(\frac {8}{3})^4×(\frac {3}{4})^4=(\frac {8}{3}×\frac {3}{4})^4=2^4=16；$?
?$ ②(-\frac {1}{2})^{-3}×2^{-4}-4^{-2}×(-0.25)^{-3}$?
?$=(-2)^3×(\frac {1}{2})^4-(\frac {1}{4})^2×(-4)^3$?
?$ =[(-2)×\frac {1}{2}]^3×\frac {1}{2}-[\frac {1}{4}×(-4)]^2×(-4)$?
?$ =-\frac {1}{2}-(-4)$?
?$ =-\frac {1}{2}+4$?
?$ =3\frac {1}{2}$?
解：?$①$?當(dāng)?$2x + 3 = 1$?時(shí)，解得?$x = -1，$?
此時(shí)?$x + 2024 = 2023，$?
則?$(2x + 3)^{x + 2024}=1^{2023}=1，$?
所以?$x = -1；$?
?$ ②$?當(dāng)?$2x + 3 = -1$?時(shí)，解得?$x = -2，$?
此時(shí)?$x + 2024 = 2022，$?
則?$(2x + 3)^{x + 2024}=(-1)^{2022}=1，$?
所以?$x = -2；$?
?$ ③$?當(dāng)?$x + 2024 = 0$?時(shí)，?$x = -2024，$
?此時(shí)?$2x + 3 = -4045，$
?則?$(2x + 3)^{x + 2024}=(-4045)^0=1，$?
所以?$x = -2024。$?
綜上所述，當(dāng)?$x = -1$?或?$x = -2$?或?$x = -2024$?時(shí)，
代數(shù)式?$(2x + 3)^{x + 2024}$?的值為?$1。$?
解：設(shè)?$S = 1 + 3^{-1} + 3^{-2} + … + 3^{-1000}，$?
?$ $?所以?$3S = 3×(1 + 3^{-1} + 3^{-2} +…+ 3^{-1000}) $?
?$= 3 + 1 + 3^{-1} + 3^{-2} +… + 3^{-999}，$?
?$ $?所以?$2S=(3 + 1 + 3^{-1} + 3^{-2} + … + 3^{-999})-$?
?$(1 + 3^{-1} + 3^{-2} + … + 3^{-1000}) $?
?$= 3 - 3^{-1000}，$?
?$ $?所以?$S=\frac {3 - 3^{-1000}}{2}。$?

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