(i) \(\frac{-125}{729}\)
We have,
= \(-\) \(\frac{-125}{729}\)
= \(-\frac{\sqrt[3]{5\times5\times5}}{\sqrt[3]{9\times9\times9}}\)
= \(-\frac{\sqrt[3]{5^3}}{\sqrt[3]{7^3}}\)
= \(-\frac{5}{7}.\)
(ii) \(\frac{10648}{12167}\)
By getting prime factors of given problems.
We have,
= \(\sqrt[3]{\frac{10648}{12167}}\)
= \(\frac{\sqrt[3]{2\times2\times2\times11\times11\times11}}{\sqrt[3]{23\times23\times23}}\)
= \(\frac{\sqrt[3]{2^3\times11^3}}{\sqrt[3]{23^3}}\)
= \(\frac{2\times11}{23}\)
= \(\frac{22}{23}.\)
(iii) \(\frac{-19683}{24384}\)
By getting prime factors of given problems.
We have,
= \(\frac{-19683}{24384}\)
= \(-\frac{\sqrt[3]{3\times3\times3\times3\times3\times3\times3\times3\times3}}{\sqrt[3]{29\times29\times29}}\)
= \(-\frac{\sqrt[3]{2^3\times11^3}}{\sqrt[3]{29^3}}\)
= \(-\frac{(3\times3\times3)}{29}\)
= \(-\frac{27}{29}\)
(iv) \(\frac{686}{-3456}\)
By getting prime factors of given problems.
We have,
= \(\frac{686}{-3456}\)
= \(-\frac{\sqrt[3]{2\times7\times7\times7}}{\sqrt[3]{2^7\times2^3}}\)
= \(-\frac{\sqrt[3]{2\times7^3}}{\sqrt[3]{2^7\times2^3}}\)
= \(-\frac{\sqrt[3]{7^3}}{\sqrt[3]{2^6\times263}}\)
= \(\frac{-7}{2\times2\times2\times2}\)
(v) \(\frac{-39304}{-42875}\)
By getting prime factors of given problems.
We have,
