Rewriting Powers with Negative Exponents: Sequence-Based Construction
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This GeoGebra example demonstrates how to apply the negative exponent rule to rewrite power expressions into equivalent fractional forms, and how the resulting values can be organized and visualized as a generated sequence. The key mathematical concepts include negative exponent laws (a^(-n) = 1/a^n), rational number representation, and algebraic equivalence through fraction rewriting. Construction-wise, the example is based on the GeoGebra commands reflected in the provided construction summary: the “Sequence” command creates the object f as a sequence of values tied to the negative exponents, and the listed/parameter object l1 is used to control or store the relevant sequence structure for display. Suitable for middle to high school algebra, exponents and rational number units, as well as homework review and exploratory learning using dynamic math software.
GeoGebra Commands & Parameters
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 Drawing Prompt Reference
Draw a function graph showing the sequence of values for a negative exponent function from -100 to 100. The sequence is based on the negative exponent rule, rewriting power expressions into fractional forms. The graph should clearly illustrate how the function values approach zero as the exponent increases negatively and grow rapidly in the positive exponent region, demonstrating the characteristics of negative exponent functions.
The prompt above was compiled from the original drawing commands and is for reference only.