AQyaaya - 13 ivaYaya - gaiNat kxaa - saatvaIM GaataMk AaOr Gaat

ivaYaya - saUcaI o hO o Gaat evaM AaQaar o ]dahrNa o AByaasa

hO bahut baD,I saM#yaaAaoM kao pZ,naa bahut mauiSkla haota hO.[na saM#yaaAaoM kao pZ,nao ko ilae hma Gaat ka p`yaaoga krto hOM.

Gaat evaM AaQaar 1,00,000 = 10x10x10x10x10 =10 5 yaha^M 10 AaQaar (Base) hO AaOr 5 GaataMk (Power) khlaata hO. yaa 10 kI 5vaIM Gaat pZ,a jaata hO.

]dharNa kao 2 kI Gaat maoM vyakt kIijae. 256 =2x2x2x2x2x2x2x2 hma kh sakto hOM ik 256 =2 8

]dharNa 2 kaOna saa AMk baD,a hO 2 3 yaa =2x2x2=8 3 2 =3x3=9 At: 2 3 < 3 2

]dharNa kao 2 kI Gaat maoM vyakt kIijae. 128 =2x2x2x2x2x2x2 hma kh sakto hOM ik 128 =2 7

]dharNa 4 kaOna saa AMk baD,a hO 2 8 yaa =2x2x2x2x2x2x2x2= =8x8=64 At: 2 8 > 8 2

]dharNa 5 a 4 b 2 kao p`saairt $p maoM ilaiKe. =(axaxaxa) x (bxb) =a x a x a x a x b x b

GaataMka oM ko inayama 1. ek hI AaQaar vaalao GaataMkaoM ka gauNana 2. ek hI AaQaar vaalao GaataMkaoM ka ivaBaajana 3. ek Gaat kI Gaat laonaa 4. samaana GaataMkaoM vaalaI GaataoM ka gauNana 5. samaana GaataMkaoM vaalaI GaataoM ka ivaBaajana

ek hI AaQaar vaalao GaataMkaoM ka gauNana 2 3 x 2 2 maoM AaQaar samaana hO. At: gauNaa krto samaya [na kI Gaat ka yaaoga haota hO. At: 2 3 x 2 2 = x 2 2 =(2x2x2) x (2x2) =2x2x2x2x2 =32

Qyaana idijae. 2 3 x 3 2 maoM AaQaar samaana nahIM hO. At: gauNaa krto samaya [na kI Gaat ka yaaoga nahIM haogaa.

ek hI AaQaar vaalao GaataMkaoM ka ivaBaajana 2 4 /2 2 maoM AaQaar samaana hO. At: Baaga krto samaya [na kI Gaat ka GaTa haota hO. At: 2 5 /2 2 = x 2 2 =(2x2x2x2x2) / (2x2) = 2x2x2x2x2 2x2 = 2x2x2 =8

ek Gaat kI Gaat laonaa (2 3 ) 2 ka Aqa- hO 2 3 ka svayaM sao dao baar gauNaa hao jaanaa. At: 2 3 x 2 3 =2 a m x a n =a m+n haota hO. =2 3+3 =2 6 Aqaa-t 2 3x2

samaana GaataMkaoM vaalaI GaataoM ka gauNana 2 3 x 3 3 maoM GaataMk samaana hO. yaha^M GaataoM ko AaQaar iBanna hO. 2 3 x 3 3 =(2x2x2) x (3x3x3) =(2x3) x (2x3) x (2x3) =6x6x6 = AaQaaraoM 2 AaOr 3 ka gauNanafla hO.

samaana GaataMkaoM vaalaI GaataoM sao ivaBaajana

ABya asa

ABya asa 1 GaataMkaoM ko inayamaaoM ka p`yaaoga kr ko hla kIijae. 3 4 x 3 3 a 3 x a 3 (5 3 ) 2 / 5 3 (2 10 / 2 7 )x 2 2

ABya asa 2 sqaana Baire maoM AaQaar hO AaOr Gaat hO. 2 3 x 3 3 maoM samaana nahIM hO. AaQaar samaana haonao pr gauNaa krto samaya Gaat ka haota hO. (2 3 ) 2 ka Aqa- hO 2 3 ka svayaM sao baar hao jaanaa.

ABya asa 2 sqaana Baire maoM AaQaar 10 hO AaOr Gaat 5 hO. 2 3 x 3 3 maoM AaQaar samaana nahIM hO. AaQaar samaana haonao pr gauNaa krto samaya Gaat ka yaaoga haota hO. (2 3 ) 2 ka Aqa- hO 2 3 ka svayaM sao dao baar gauNaa hao jaanaa.

Qan yava ad