पढ़ें- गणित के महत्त्वपूर्ण टॉपिक घातांक(Indices) - घातांक की परिभाषा तथा घातांकके 6 नियम - घातांकीय गुणनफल का नियम, घातांकीय भाग का नियम.....उदाहरण सहित
घात अथवा घातांक (Indices) :-घातांक का सामान्य अर्थ है , जिस संख्या के ऊपर जो संख्या (घात) है, उस संख्या को उतनी बार गुणा करना, जितनी उसके ऊपर संख्या (घात) है।
माना कोई संख्या a है जिसको n बार गुणा किया जाता है |
⇒a x a x a x a……..x a( n बार ) = an
जहाँ a वास्तविक संख्या है जिसको आधार (Base) तथा n को घातांक (Indices) कहते हैं |
उदाहरण: 35 = 5 x 5 x 5 x 5 x 5
घातांक (Indices)
माना कोई संख्या a है जिसको n बार गुणा किया जाता है |
⇒a x a x a x a……..x a( n बार ) = an
जहाँ a वास्तविक संख्या है जिसको आधार (Base) तथा n को घातांक (Indices) कहते हैं |
उदाहरण: 35 = 5 x 5 x 5 x 5 x 5
घातांक की परिभाषा | Deffination of Indices in Hindi
" किसी वास्तविक संख्या को उसी संख्या से जितनी बार गुणा किया जाता है तो जितने बार गुणा किया जाता है तो उसे उस संख्या का घातांक कहते हैं और जिस संख्या को गुणा किया जाता है उसे उस घातांक का आधार कहलाता है |"
![घातांक के नियम1 घातांक के नियम1](data:image/png;base64,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)
(since
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![Indices rule Indices rule](data:image/png;base64,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)
amxan=am+n
2. घातांकीय भाग का सूत्र:
am / an = am / an = am-n
3. घात की घात का गुणनफल का सूत्र:
{(am)n}p = amnp
4. गुणनफल की घात का सूत्र:
(a x b x c)n=(an x bn x cn)
5. घात के व्युत्क्रम का सूत्र:
am= 1/ a-m
6. शून्य घात का सूत्र:
a0 = 1
7. व्युत्क्रम घात का सूत्र:
यदि an = b
तो a = a1/b
an = a x a x a
x a x a x a x a……………….(n गुरणखंण्ड)
➩ मुख्य बिंदु (IMPORTANT POINTS) :
घातांक के 6 नियम
नियम
1:
0 के अतिरिक्त कोई भी संख्या जिसकी घात शून्य हो गी तो उसका
मान 1 के बराबर होगा
उदाहरण:
सरल करो 20:
नियम2: |
उदाहरण:
सरल करो: 2-2
नियम 3:
अगर घात वाली
संख्याओं को परस्पर गुणा किया गया हो और आधार सामान तो घातें आपस में जुड़ जाती हैं ।
उदाहरण:
सरल करो:
(note: 5 = 51)
नियम 4:
अगर घात वाली
संख्याओं को परस्पर भाग किया गया हो और आधार सामान तो घातें आपस में घट जाती हैं ।
उदाहरण:
सरल करो
|
:
|
नियम 5 :
अगर किसी घात वाली
संख्या पुनः घात किया गया हो और तो घातें आपस में गुणा हो जाती हैं ।
उदाहरण:
सरल करो (y2)6:
नियम 6: |
उदाहरण:
सरल करो 1252/3:
घातांक के महत्त्वपूर्ण तथा उपयोगी सूत्र | Important Formula of Indices in Hindi
1. घातांकीय गुणनफल का सूत्र :amxan=am+n
2. घातांकीय भाग का सूत्र:
am / an = am / an = am-n
3. घात की घात का गुणनफल का सूत्र:
{(am)n}p = amnp
4. गुणनफल की घात का सूत्र:
(a x b x c)n=(an x bn x cn)
5. घात के व्युत्क्रम का सूत्र:
am= 1/ a-m
6. शून्य घात का सूत्र:
a0 = 1
7. व्युत्क्रम घात का सूत्र:
यदि an = b
तो a = a1/b
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