Degree izinombolo: umlando, definition, izakhiwo eyisisekelo

Indlela elula izinkulumo zezibalo yaziwa abantu kusukela ezikhathini zasendulo. Ngesikhathi esifanayo njalo lidlule ekuthuthukiseni kokubili imisebenzi acophe kubo esithwalini ethile.

Ikakhulukazi, eGibhithe lasendulo, ogama ososayensi baye babamba iqhaza elikhulu esemqoka ekuthuthukisweni kwe-arithmetic aphansi, futhi ebeka izisekelo algebra futhi geometry, yabhekisela yokuthi uma kukhona ukuphindwaphindwa kwanoma yisiphi isibalo ngomunye futhi inani elifanayo ngokuphindaphindiwe, bese ichithe omningi umzamo ezingadingekile. Ngaphezu kwalokho, lo msebenzi kwaholela izindleko ngemali okukhulu: ngokuvumelana ke uthatha isinyathelo Umklamo ukufaka yanoma yimuphi amarekhodi isenzo ngasinye inombolo okufanele ichazwe ngokuningiliziwe. Uma sikhumbula ukuthi ngisho elula-papyrus izindleko impela esikhulu semali, bese-ke, akumangalisi ukuthi leyo mizamo yabo, okwathi abaseGibithe bekulinga lokho ozenze ukuthola indlela yokuphuma kulesi simo.

Isinqumo bathole Diophantus odumile wase-Aleksandriya, abenyukela isibonakaliso esikhethekile zezibalo, okuyinto waqala ukubonisa kukangaki kumelwe wande lokhu noma lokhuya inombolo ngokwalo. Ngemva kwalokho, isazi sezibalo esidumile French Descartes ngcono ukuba kubhalwe le nkulumo, okusikisela e ekubizweni ngezinga izinombolo nje baxhumanisa lokho ekhoneni eliphezulu kwesokudla ngenhla inombolo enkulu.

Kuzithinta yokugcina ifomu ebhaliwe izinombolo ngokwezinga kwaba umsebenzi we N. eziyihlazo Shyuke, eyethula lapho kugumbuqelwa umbuso yesayensi lokuqala ezimbi bese zero degree.

Lisho ukuthini igama elithi "ukwakha degree"? Okokuqala sidinga ukuqonda lokho kukodwa Exponentiation ingenye ezibaluleke kakhulu kanambambili imisebenzi zezibalo, ngokuyisisekelo okuyinto okuphindaphindiwe ukubuyabuyelela yenombolo ngokwalo.

Lo msebenzi ezikhonjiswe «XY» nkulumo ifomu elivamile. Kulokhu, lo «X» kuyothiwa base ezingeni, futhi «Y» - sibalo sakhe. Kulesi simo "ophakanyiswe emandleni" ngeke ukukhishwa ngokuthi "iphindwe« X »ngokwalo« Y »izikhathi."

izinombolo Degree, njengabanye izakhi kakhulu zezibalo anezici ezithile:

1. Lapho ukwakha zero degree yanoma iyiphi inombolo ngaphandle oholayo (okuhle nokubi) izovuleka iyunithi.

^^ x 0 = 1

2. Degrees izinombolo, lapho zinkomba ezingezinhle, kufanele siguqulwe ukubonakaliswa inkomba omuhle

x-a = 1 / x ^ a

3. Ukuze afeze ukubuyabuyelela izinombolo nge amandla, kufanele sikhumbule ukuthi lo msebenzi kungenzeka kuphela uma base efanayo. Ngakho ukubuyabuyelela izinombolo lamadigri Kwenziwa ngokuvumelana mithetho elandelayo: base uhlala ingashintshiwe, bese yengezwa ukubaluleka Inkomba degrees asele ukusebenza.

x ^ yx ^ z = x ^ y + z

4. Esimweni lapho kukhona ukwahlukana kwamandla, kubalulekile ukuba banamathele imithetho efanayo, ngaphandle ukuthi esikhundleni isamba kule exponent kuyoba umehluko.

x ^ y / x ^ z = x ^ YZ

5. Enye ezibalulekile impahla ngezinga ezihlotshaniswa nalezo zimo lapho udinga ukwakha degree of self okungekho. Kulokhu-ke kuyadingeka ukuba azale ande kokubili okungu.

(X ^ y) ^ z = x ^ YZ

6. Kwezinye izimo, kunesidingo ukupenda degree of umkhiqizo ngokusebenzisa izinombolo degree. Kulokhu, kufanele sikhumbule ukuthi lokuphuma phambili okumisiwe umkhiqizo ibalwa ngokuhambisana nalo mthetho lapha:

(Xyz) ^ a = x ^ ay ^ az ^ a

7. Uma udinga upende ubukhulu yangasese, into yokuqala kufanele uqaphele ukuthi ngesisekelo Iningi abakwazi ukuba uziro. Kungenjalo-ke kuyadingeka ukuba banamathele fomula elandelayo:

(X / y) ^ a = x ^ a / y ^ a

nobunzima athile ihlangabezane uma liyadingeka ukwakha isisekelo amandla, uwukubonakaliswa okuyinto esingaphansi zero. Umphumela kulokhu kungase kube mubi noma ube muhle. It kuzoncika eksponenti, okungukuthi kulokho inombolo - akukuhle noma ngisho - lokhu babengamaphesenti.