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What is (64^{2/3})?(64^{2/3}) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 1616
Using the rule for fractional exponents, \(64^{2/3}=(\sqrt[3]{64})^2\). Since \(\sqrt[3]{64}=4\), we get \(4^2=16\). Therefore, option B is correct. Option A is only the cube root and does not include the required squaring. Exam tip: For \(a^{m/n}\), it is often easiest to take the \(n\)th root first and then raise the result to the \(m\)th power.घात के नियम के अनुसार, \(64^{2/3}=(\sqrt[3]{64})^2\)। चूँकि \(\sqrt[3]{64}=4\), इसलिए \(4^2=16\)। अतः सही उत्तर विकल्प B है। विकल्प A में केवल घनमूल लिया गया है, वर्ग नहीं किया गया। परीक्षा-युक्ति: \(a^{m/n}\) में पहले \(n\)वाँ मूल लेकर फिर \(m\)वीं घात करना सुविधाजनक होता है।
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