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If \(x^4=5\), what is the value of \(x^{12}-x^8\)?यदि \(x^4=5\), तो \(x^{12}-x^8\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 100100
Using the laws of exponents, \(x^{12}=(x^4)^3=5^3=125\) and \(x^8=(x^4)^2=5^2=25\). Therefore, \(x^{12}-x^8=125-25=100\), so option C is correct. Option D is only the value of \(x^{12}\), not of the complete expression. Exam tip: When the required exponents are multiples of a given exponent, rewrite them as powers of that given expression.घातों के नियम से \(x^{12}=(x^4)^3=5^3=125\) और \(x^8=(x^4)^2=5^2=25\)। अतः \(x^{12}-x^8=125-25=100\), इसलिए सही विकल्प C है। विकल्प D केवल \(x^{12}\) का मान है, पूरे व्यंजक का नहीं। परीक्षा-युक्ति: जब घात दिए गए घात के गुणज हों, तो उन्हें उसी आधार-घात की शक्तियों में लिखें।
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