用负指数改写幂表达式：数列化构造与分式关系可视化
几何画板及绘图内容加载中，请稍等……
该范例用于演示如何利用负指数规则把幂运算改写为分式形式，并进一步观察由此得到的数值序列或规律。核心数学概念包括：负指数幂 a^(-n) = 1/a^n 的等价变形、分数与有理数的表示、指数运算的代数恒等变形。作图要点是从构造摘要提炼的 GeoGebra 思路：使用“Sequence”命令生成一组与负指数相关的数值对象（对象 f），再配合“对对象 l1”所对应的列表/参数对象（即命令中给出的 l1）组织并展示结果的变化。适合中学阶段（代数、指数运算与有理数）教学，也可用于课堂复习、作业讲评或借助动态几何/图形软件进行规律发现与验证。
GeoGebra 命令及参数
Sequence((i, f(i)), i, -100, 100) → l1, {(-100, 9.466330862652142E-28), (-99, 1.8932661725304283E-27), (-98, 3.786532345060857E-27), (-97, 7.573064690121713E-27), (-96, 1.5146129380243427E-26), (-95, 3.0292258760486853E-26), (-94, 6.058451752097371E-26), (-93, 1.2116903504194741E-25), (-92, 2.4233807008389483E-25), (-91, 4.8467614016778965E-25), (-90, 9.693522803355793E-25), (-89, 1.9387045606711586E-24), (-88, 3.877409121342317E-24), (-87, 7.754818242684634E-24), (-86, 1.550963648536927E-23), (-85, 3.101927297073854E-23), (-84, 6.203854594147708E-23), (-83, 1.2407709188295415E-22), (-82, 2.481541837659083E-22), (-81, 4.963083675318166E-22), (-80, 9.926167350636332E-22), (-79, 1.9852334701272664E-21), (-78, 3.970466940254533E-21), (-77, 7.940933880509066E-21), (-76, 1.588186776101813E-20), (-75, 3.176373552203626E-20), (-74, 6.352747104407253E-20), (-73, 1.2705494208814505E-19), (-72, 2.541098841762901E-19), (-71, 5.082197683525802E-19), (-70, 1.0164395367051604E-18), (-69, 2.032879073410321E-18), (-68, 4.065758146820642E-18), (-67, 8.131516293641283E-18), (-66, 1.6263032587282567E-17), (-65, 3.252606517456513E-17), (-64, 6.505213034913027E-17), (-63, 1.3010426069826053E-16), (-62, 2.6020852139652106E-16), (-61, 5.204170427930421E-16), (-60, 1.0408340855860843E-15), (-59, 2.0816681711721685E-15), (-58, 4.163336342344337E-15), (-57, 8.326672684688674E-15), (-56, 1.6653345369377348E-14), (-55, 3.3306690738754696E-14), (-54, 6.661338147750939E-14), (-53, 1.3322676295501878E-13), (-52, 2.6645352591003757E-13), (-51, 5.329070518200751E-13), (-50, 1.0658141036401503E-12), (-49, 2.1316282072803006E-12), (-48, 4.263256414560601E-12), (-47, 8.526512829121202E-12), (-46, 1.7053025658242404E-11), (-45, 3.410605131648481E-11), (-44, 6.821210263296962E-11), (-43, 1.3642420526593924E-10), (-42, 2.7284841053187847E-10), (-41, 5.456968210637569E-10), (-40, 1.0913936421275139E-9), (-39, 2.1827872842550278E-9), (-38, 4.3655745685100555E-9), (-37, 8.731149137020111E-9), (-36, 1.7462298274040222E-8), (-35, 3.4924596548080444E-8), (-34, 6.984919309616089E-8), (-33, 1.3969838619232178E-7), (-32, 2.7939677238464355E-7), (-31, 5.587935447692871E-7), (-30, 0.0000011175870895385742), (-29, 0.0000022351741790771484), (-28, 0.000004470348358154297), (-27, 0.000008940696716308594), (-26, 0.000017881393432617188), (-25, 0.000035762786865234375), (-24, 0.00007152557373046875), (-23, 0.0001430511474609375), (-22, 0.000286102294921875), (-21, 0.00057220458984375), (-20, 0.0011444091796875), (-19, 0.002288818359375), (-18, 0.00457763671875), (-17, 0.0091552734375), (-16, 0.018310546875), (-15, 0.03662109375), (-14, 0.0732421875), (-13, 0.146484375), (-12, 0.29296875), (-11, 0.5859375), (-10, 1.171875), (-9, 2.34375), (-8, 4.6875), (-7, 9.375), (-6, 18.75), (-5, 37.5), (-4, 75), (-3, 150), (-2, 300), (-1, 600), (0, 1200), (1, 2400), (2, 4800), (3, 9600), (4, 19200), (5, 38400), (6, 76800), (7, 153600), (8, 307200), (9, 614400), (10, 1228800), (11, 2457600), (12, 4915200), (13, 9830400), (14, 19660800), (15, 39321600), (16, 78643200), (17, 157286400), (18, 314572800), (19, 629145600), (20, 1258291200), (21, 2516582400), (22, 5033164800), (23, 10066329600), (24, 20132659200), (25, 40265318400), (26, 80530636800), (27, 161061273600), (28, 322122547200), (29, 644245094400), (30, 1288490188800), (31, 2576980377600), (32, 5153960755200), (33, 10307921510400), (34, 20615843020800), (35, 41231686041600), (36, 82463372083200), (37, 164926744166400), (38, 329853488332800), (39, 659706976665600), (40, 1319413953331200), (41, 2638827906662400), (42, 5277655813324800), (43, 10555311626649600), (44, 21110623253299200), (45, 42221246506598400), (46, 84442493013196800), (47, 168884986026393600), (48, 337769972052787200), (49, 675539944105574400), (50, 1351079888211148800), (51, 2702159776422297600), (52, 5404319552844595200), (53, 10808639105689190000), (54, 21617278211378380000), (55, 43234556422756760000), (56, 86469112845513520000), (57, 172938225691027050000), (58, 345876451382054100000), (59, 691752902764108200000), (60, 1.3835058055282164E+21), (61, 2.767011611056433E+21), (62, 5.534023222112865E+21), (63, 1.106804644422573E+22), (64, 2.213609288845146E+22), (65, 4.427218577690292E+22), (66, 8.854437155380585E+22), (67, 1.770887431076117E+23), (68, 3.541774862152234E+23), (69, 7.083549724304468E+23), (70, 1.4167099448608936E+24), (71, 2.833419889721787E+24), (72, 5.666839779443574E+24), (73, 1.1333679558887149E+25), (74, 2.2667359117774297E+25), (75, 4.533471823554859E+25), (76, 9.066943647109719E+25), (77, 1.8133887294219438E+26), (78, 3.6267774588438875E+26), (79, 7.253554917687775E+26), (80, 1.450710983537555E+27), (81, 2.90142196707511E+27), (82, 5.80284393415022E+27), (83, 1.160568786830044E+28), (84, 2.321137573660088E+28), (85, 4.642275147320176E+28), (86, 9.284550294640352E+28), (87, 1.8569100589280704E+29), (88, 3.713820117856141E+29), (89, 7.427640235712282E+29), (90, 1.4855280471424563E+30), (91, 2.9710560942849127E+30), (92, 5.942112188569825E+30), (93, 1.188422437713965E+31), (94, 2.37684487542793E+31), (95, 4.75368975085586E+31), (96, 9.50737950171172E+31), (97, 1.901475900342344E+32), (98, 3.802951800684688E+32), (99, 7.605903601369376E+32), (100, 1.5211807202738753E+33)}
AI 绘图提示语参考
绘制一个函数图像，展示从负100到正100的负指数幂函数值序列。该序列基于负指数规则，将幂表达式转化为分数形式，并按数值大小排列。图像应清晰显示随着指数的增大，函数值逐渐趋近于零，并在正指数区域迅速增长，体现负指数函数的特性。
以上提示语为根据原始绘图命令整理而来，仅供参考。