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For \(x\ne0\), what is the simplified form of \(\frac{(5x^{-2})^{2}(2x^{4})^{2}}{20x^{4}}\)?जहाँ \(x\ne0\), \(\frac{(5x^{-2})^{2}(2x^{4})^{2}}{20x^{4}}\) का सरल रूप क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 55
Using the laws of exponents, \((5x^{-2})^2=25x^{-4}\) and \((2x^4)^2=4x^8\). Thus, the numerator becomes \(25x^{-4}\cdot4x^8=100x^4\). Therefore, \(\frac{100x^4}{20x^4}=5\), since \(x\ne0\). Hence, the correct answer is 5. Exam tip: square each bracket first, combine powers with the same base, and then cancel common factors.घात के नियम से \((5x^{-2})^2=25x^{-4}\) और \((2x^4)^2=4x^8\)। इसलिए अंश \(25x^{-4}\cdot4x^8=100x^4\) होगा। अब \(\frac{100x^4}{20x^4}=5\), क्योंकि \(x\ne0\)। अतः सही उत्तर 5 है। परीक्षा-युक्ति: पहले प्रत्येक कोष्ठक का वर्ग करें, फिर समान आधार वाली घातों को जोड़कर समान गुणकों को काटें।
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