分数指数幂的运算
\u5206\u6570\u6307\u6570\u5e42\u7684\u8fd0\u7b97\u4e24\u4e2a\u90fd\u6b63\u786e\uff0c\u4f60\u60f3\u6cd5\u9519\u4e86\uff0c\u221aa^3/4\u662fa^\uff083/4\uff09\u00d7\uff081/2\uff09\uff0c\u6839\u53f7\u4e0b\u7684\u6570\u662f\u4e2a\u5e42\u6307\u6570\uff0cm=3\uff0cn=4\uff0c\u591a\u4e2a\u6839\u53f7\u53ea\u662f\u5b83\u7684\u6307\u6570\u88ab\u7f29\u5c0f\u4e86\u4e00\u534a\uff0c\u6307\u6570\u8fd0\u7b97\u662f\u6307\u6570\u7684\u52a0\u51cf\u4e58\u9664\uff0c\u5e94\u8be5\u5206\u90e8\u8fdb\u884c\uff0c\u5c42\u5c42\u5265\u5f00 \uff0c\u697c\u4e3b\u60f3\u592a\u591a\u4e86\uff0c\u5f88\u5bb9\u6613\u628a\u81ea\u5df1\u5f04\u7cca\u6d82
\u4ee4m=a\u4e09\u5206\u4e4b\u4e00\u6b21\u65b9
n=b\u4e09\u5206\u4e4b\u4e00\u6b21\u65b9
\u5219m²+n²=4
x=m³+3mn²
y=n³+3m²n
\u5219x+y=m³+3m²n+3mn²+n³=(m+n)³
x-y=m³-3m²n+3mn²-n³=(m-n)³
\u6240\u4ee5(x+y)\u7684\u4e09\u5206\u4e4b\u4e8c\u6b21\u65b9=[(m+n)³]\u7684\u4e09\u5206\u4e4b\u4e8c\u6b21\u65b9=(m+n)²
(x-y)\u7684\u4e09\u5206\u4e4b\u4e8c\u6b21\u65b9 =(m-n)²
\u6240\u4ee5\u539f\u5f0f=(m+n)²+(m-n)²
=m²+2mn+n²+m²-2mn+n²
=2(m²+n²)
=8
绛旓細鍒嗘暟鎸囨暟骞傜殑杩愮畻娉曞垯鏄寚鏁板姞鍑忓簳涓嶅彉锛屽悓搴曟暟骞傜浉涔橀櫎銆1銆佸垎鏁颁负鎸囨暟鐨勮繍绠楁柟寮忔槸a鐨剎鍒唝娆℃柟锛屼篃灏辨槸a鐨剏娆℃柟鍦ㄥ紑a娆℃牴鍙凤紝渚嬪a^1/3涔熷氨鏄痑鐨1娆℃柟寮3娆℃牴鍙凤紝鍒嗘暟鎸囨暟骞傛槸涓涓暟鐨勬寚鏁颁负鍒嗘暟锛屽2鐨1/2娆″箓灏辨槸鏍瑰彿2 锛屽垎鏁版寚鏁板箓鏄牴寮忕殑鍙︿竴绉嶈〃绀哄舰寮忋2銆佹寚鏁板箓鐨勬ц川鏄换浣曢潪闆...
绛旓細鍒嗘暟鎸囨暟骞傜殑杩愮畻娉曞垯鍙敤浜庤绠楁暟鍊硷紝渚嬪璁＄畻 2^(1/2) 鐨勮繎浼煎銆傛牴鎹箻鏂圭殑鍒嗘瘝鎸囨暟娉曞垯锛屾垜浠彲浠ュ皢鎸囨暟鐨勫垎姣嶄笌 2 鐩镐箻寰楀埌 2^(1/(2*2)) = 2^(1/4) 鈮 1.189銆3. 姹傝В鏂圭▼锛氬垎鏁版寚鏁板箓鐨勮繍绠楁硶鍒欏彲浠ョ敤浜庢眰瑙ｆ柟绋嬨備緥濡傦紝鑰冭檻鏂圭▼ 3^(2x+1/4) = 9锛屾牴鎹箻鏂圭殑鍒嗘暟鎸囨暟娉曞垯鍜屼箻娉...
绛旓細1銆佸垎鏁版寚鏁板箓鐨勮绠楁柟娉曪細涓涓暟鐨刡鍒嗕箣a娆℃柟绛変簬b娆℃牴鍙蜂笅杩欎釜鏁扮殑a娆℃柟銆2銆佹牴鎹垎鏁版寚鏁板箓鐨勮绠楁柟娉曪紝寰楀埌3鐨3鍒嗕箣2娆℃柟绛変簬3娆℃牴鍙蜂笅3鐨2娆℃柟銆3銆佸嵆³鈭氾紙3²锛=³鈭9銆
绛旓細鍒嗘暟鎸囨暟骞傜殑杩愮畻娉曞垯濡備笅锛鎸囨暟鐩镐箻搴曟暟涓嶅彉锛屽箓鐨勪箻鏂圭浉涔橀櫎銆傛寚鏁板姞鍑忓簳鏁颁笉鍙橈紝鍚屽簳鏁板箓鐩镐箻闄ゃ傜Н鍟嗕箻鏂瑰師鎸囨暟锛屾崲搴曚箻鏂瑰啀涔橀櫎銆傝礋鏁存暟鐨勬寚鏁板箓锛屾寚鏁拌浆姝ｆ眰鍊掓暟銆傞潪闆舵暟鐨勯浂娆″箓锛屽父鍊间负 1涓嶇浉涔橀櫎銆傜湅鍒板垎鏁版寚鏁板箓锛屽簳鏁板繀涓洪潪璐熸暟銆備箻鏂规寚鏁版槸鍒嗗瓙锛屾牴鎸囨暟瑕佸綋鍒嗘瘝銆傚浜庝换鎰忔湁鐞嗘暟r,s,鍧...
绛旓細32^0.5 =32^1/2 =鈭32 =鈭16脳鈭2 =4鈭2 鍒嗘暟鎸囨暟骞傛槸姝ｅ垎鏁版寚鏁板箓鍜岃礋鍒嗘暟鎸囨暟骞傜殑缁熺О銆傚垎鏁版寚鏁板箓鏄竴涓暟鐨勬寚鏁颁负鍒嗘暟锛屾鏁扮殑鍒嗘暟鎸囨暟骞傛槸鏍瑰紡鐨勫彟涓绉嶈〃绀哄舰寮忋傝礋鏁扮殑鍒嗘暟鎸囨暟骞傚苟涓嶈兘鐢ㄦ牴寮忔潵璁＄畻锛岃岃鐢ㄥ埌鍏跺畠绠楁硶锛屾槸楂樹腑浠ｆ暟鐨勯噸鐐广
绛旓細璁＄畻鍒嗘暟鐨勬寚鏁板箓鍙互閫氳繃浠ヤ笅姝ラ杩涜锛1銆佸垎鏁扮殑鎸囨暟骞傚畾涔夛細瀵逛簬浠绘剰瀹炴暟 a 鍜屾鏁存暟 n锛屽叾涓 a 涓嶇瓑浜庨浂锛岃〃绀 a 鐨 n 娆℃柟銆傝繖鍚屾牱閫傜敤浜庡垎鏁般備緥濡傦紝瀵逛簬鍒嗘暟 鍜屾鏁存暟 k锛岃〃绀 2銆佽绠楀垎瀛愬拰鍒嗘瘝鐨勫悇鑷箓锛氬皢鍒嗘暟鐨勫垎瀛愬拰鍒嗘瘝鍒嗗埆杩涜鎸囨暟骞傝繍绠銆備緥濡傦紝瀵逛簬 璁＄畻鍒嗗瓙 鍜屽垎姣 寰 3銆佸寲绠...
绛旓細鍒嗘暟鎸囨暟骞傛槸涓涓暟鐨勬寚鏁颁负鍒嗘暟锛屽2鐨1/2娆″箓灏辨槸鏍瑰彿2銆傚垎鏁版寚鏁板箓鏄牴寮忕殑鍙︿竴绉嶈〃绀哄舰寮忥紝鍗硁娆℃牴鍙(a鐨刴娆″箓)鍙互鍐欐垚a鐨刴/n娆″箓銆傛牴鎹鍒嗘暟鎸囨暟骞傜殑瀹氫箟锛屽彲寰楋細10鐨勪笁鍒嗕箣浜屾鏂=10^(2/3)=³鈭氾紙10²锛=³鈭100銆傛鏁扮殑鍒嗘暟鎸囨暟骞傛槸鏍瑰紡鐨勫彟涓绉嶈〃绀哄舰寮忋傝礋鏁扮殑...
绛旓細寮曞叆鍒嗘暟鎸囨暟骞傚苟灏骞傜殑杩愮畻鎬ц川鎺ㄥ箍鍒版湁鐞嗘暟鐨勬剰涔夛紝灏嗕箻鏂逛笌寮鏂圭殑杩愮畻缁熶竴涓哄悓涓绉嶈繍绠楋紝鍗冲箓鐨勮繍绠椼傚浜庤绠楃粨鏋滐紝骞朵笉寮烘眰鐢ㄧ粺涓鐨勫舰寮忔潵琛ㄧず锛屽鏋滄病鏈夌壒鍒殑瑕佹眰锛屼竴鑸敤鍒嗘暟鎸囨暟骞傜殑褰㈠紡琛ㄧず銆備絾缁撴灉涓嶈兘鍚屾椂鍚湁鏍瑰紡鍜屽垎鏁版寚鏁帮紝涔熶笉鑳芥棦鏈夊垎姣嶅張鍚湁璐熸寚鏁般備互涓婃槸鍒嗘暟骞傜殑鍩烘湰璁＄畻瑙勫垯銆傞渶瑕...
绛旓細1. 鍒嗘暟鎸囨暟骞傜殑鎰忎箟鐩殑灏辨槸浣垮叾鎸囨暟鐨勮繍绠灏侀棴鎬с傛墍浠ュ皝闂э紝灏辨槸鍥犱负鎸囨暟杩愮畻婊¤冻锛(a^m)^n=a^(m*n)鍙湁鍒嗘暟鎸囨暟骞傚畾涔変负鏍瑰紡锛屾墠鑳芥弧瓒充笂闈㈡ц川锛掞紟鎴戜笉鐭ヤ綘鏄垵涓繕鏄珮涓鐢燂紟瀵逛簬鍒濅腑瀛︾敓鏉ヨ锛岃礋鏁版槸涓嶈璁哄垎鏁版寚鏁板箓锛岃繖鐢变簬鏍瑰彿-1锛堜篃灏辨槸璐燂紤鐨勪簩鍒嗕箣涓娆″箓锛夋槸娌℃湁鎰忎箟锛屼笉瀛樺湪...
绛旓細鍒嗘暟鐨勬寚鏁板箓鐨勮繍绠娉曞垯鍙互閫氳繃浠ヤ笅姝ラ杩涜锛氬鍒嗘暟鐨勫垎瀛愬拰鍒嗘瘝鍒嗗埆杩涜鎸囨暟骞傝繍绠楋紝鍗冲皢鎸囨暟搴旂敤浜庡垎瀛愬拰鍒嗘瘝涓殑鏁板奸儴鍒嗐傚寲绠鎸囨暟骞傝繍绠楀悗鐨勫垎瀛愬拰鍒嗘瘝锛屽鏋滃彲鑳界殑璇濓紝灏嗗叾绾﹀垎鑷虫渶绠褰㈠紡銆傚鏋滄寚鏁颁负姝ｆ暟锛屽垯淇濈暀鍒嗘暟褰㈠紡銆傚鏋滄寚鏁颁负璐熸暟锛屽垯灏嗗垎鏁板掔疆锛屽苟灏嗘寚鏁版敼涓烘鏁般備緥濡傦紝瀵逛簬鍒嗘暟 a/b ...
