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What is the simplified form of \(\frac{2a^{-1}+3a^{-1}}{5a^{-2}}\), where \(a\neq 0\)?\(\frac{2a^{-1}+3a^{-1}}{5a^{-2}}\) का सरल रूप क्या है, जहाँ \(a\neq 0\)?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(a\)\(a\)
Combining like terms gives \(2a^{-1}+3a^{-1}=5a^{-1}\). Therefore, \(\frac{5a^{-1}}{5a^{-2}}=a^{-1-(-2)}=a^1=a\), so option A is correct. Exam tip: when dividing powers with the same non-zero base, subtract the exponents: \(a^m/a^n=a^{m-n}\).समान पदों को जोड़ने पर \(2a^{-1}+3a^{-1}=5a^{-1}\)। अतः \(\frac{5a^{-1}}{5a^{-2}}=a^{-1-(-2)}=a^1=a\)। इसलिए सही उत्तर विकल्प A है। ध्यान रखें कि समान आधारों के भाग में घातें घटाई जाती हैं: \(a^m/a^n=a^{m-n}\)।
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