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Q. Find the value of \( \left(\frac{169^{-3}}{196^{-8}}\right)^{\frac{1}{48}} \)
✏️ Solution
\( = \left(\frac{(13^2)^{-3}}{(14^2)^{-8}}\right)^{\frac{1}{48}} \)
\( = \left(\frac{13^{-6}}{14^{-16}}\right)^{\frac{1}{48}} \)
\( = \left(13^{-6} \times 14^{16}\right)^{\frac{1}{48}} \)
\( = 13^{-\frac{6}{48}} \times 14^{\frac{16}{48}} \)
\( = 13^{-\frac{1}{8}} \times 14^{\frac{1}{3}} \)
\( = \frac{14^{1/3}}{13^{1/8}} \)
Final Answer: \( \boxed{\dfrac{14^{1/3}}{13^{1/8}}} \)