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If \(x^5=3\), what is the value of \(x^{15}+x^{10}\)?यदि \(x^5=3\) है, तो \(x^{15}+x^{10}\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 3636
Using the laws of exponents, \(x^{15}=(x^5)^3=3^3=27\) and \(x^{10}=(x^5)^2=3^2=9\). Hence, \(x^{15}+x^{10}=27+9=36\), so option B is correct. Exam tip: rewrite each exponent as a multiple of 5 before substituting the given value of \(x^5\).घातांक के नियम से \(x^{15}=(x^5)^3=3^3=27\) और \(x^{10}=(x^5)^2=3^2=9\)। अतः \(x^{15}+x^{10}=27+9=36\), इसलिए विकल्प B सही है। ध्यान रखें कि \(x^{mn}=(x^m)^n\) का प्रयोग करते समय दिए गए \(x^5\) को उचित घात तक उठाना चाहिए।
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