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घातांक और घात

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Question
CBSEHENMAH8003568
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घातांकों का उपयोग करते हुए निम्न को विस्तारित रूप में लिखिए।
(i) 1025.63
(ii) 1256.249

Solution

(i)  1025.63 space equals space 1 space cross times space 1000 space plus space 2 space cross times space 10 space plus space 5 space cross times space 1 space plus space 6 over 10 plus 3 over 100
              equals 1 cross times 10 cubed plus 2 cross times 10 plus 5 cross times 1 plus 6 cross times 10 to the power of negative 1 end exponent plus 3 cross times 10 to the power of negative 2 end exponent
(ii)    1256.249 space equals space 1 space cross times space 1000 space plus space 2 space cross times space 100 space plus space 5 space cross times space 10 space plus space 6 space cross times space 1
                           plus 2 cross times 1 over 10 plus 4 cross times 1 over 100 plus 9 cross times 1 over 1000
                       equals 1 cross times 10 cubed plus 2 cross times 10 squared plus 5 cross times 10 plus 6 cross times 1 plus 2 cross times 10 to the power of negative 1 end exponent plus 4 cross times 10 to the power of negative 2 end exponent plus 9 cross times 10 to the power of negative 3 end exponent

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Question
CBSEHHIMAH8003948
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गुणात्मक प्रतिलोम लिखिए:
(i) 2–4            (ii) 10–5         (iii) 7–2    (iv) 5–3   (v) 10–100

Solution

a का गुणात्मक प्रतिलोम  1 over straight a है।अत:
(i) 2-4 का गुणात्मक प्रतिलोम है   1 over 2 to the power of negative 4 end exponent space equals space 2 to the power of 4
(ii) 10-5 का गुणात्मक प्रतिलोम है   1 over 10 to the power of negative 5 end exponent space equals space 10 to the power of 5
(iii) 7-2 का गुणात्मक प्रतिलोम है  1 over 7 to the power of negative 2 end exponent equals space 7 squared
(iv) 5-3 का गुणात्मक प्रतिलोम है  1 over 5 to the power of negative 3 end exponent space equals space 5 cubed
(v) 10-100 का गुणात्मक प्रतिलोम है  1 over 10 to the power of negative 100 end exponent space equals space 10 to the power of 100

Question
CBSEHHIMAH8003951
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घातांक रूप को सरल कीजिए और लिखिए:
(–2)–3 x (–2)–4

Solution

हम जानते हैं कि a (जो शून्य नहीं है) पूर्णांक है और  m, n पूर्णांक हैं, तो am x an = am+n
(–2)–3 x (–2)–4  = (-2)(-3)+(-4) =(-2)-7
  equals space fraction numerator 1 over denominator left parenthesis negative 2 right parenthesis to the power of 7 end fraction space equals fraction numerator 1 over denominator left parenthesis negative 1 right parenthesis to the power of 7 cross times left parenthesis 2 right parenthesis to the power of 7 end fraction equals space fraction numerator 1 over denominator negative 1 space cross times left parenthesis 2 right parenthesis to the power of 7 end fraction space equals space minus 1 over 2 to the power of 7           

                             

Question
CBSEHHIMAH8003952
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घातांक रूप को सरल कीजिए और लिखिए:
p3 x p–10

Solution

हम जानते हैं कि a (जो शून्य नहीं है) पूर्णांक है और  m, n पूर्णांक हैं, तो am x an = am+n
p3 x p–10= left parenthesis straight p right parenthesis to the power of 3 plus space left parenthesis negative 10 right parenthesis end exponent space equals left parenthesis straight p right parenthesis to the power of negative 7 end exponent or space fraction numerator 1 over denominator left parenthesis straight p right parenthesis to the power of 7 end fraction

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