Question

Rationalize $5^{ \frac{1}{3} } - 5^{ \frac{- 1}{3} }$ with its rationalizing factor

Answer 1

$X=5^{\frac{1}{3}} - 5^{\frac{-1}{3}}\\\\=5^{\frac{1}{3}} - \frac{1}{5^{\frac{1}{3}}}\\\\=\frac{5^{\frac{2}{3}}-1}{5^{\frac{1}{3}}}\\\\=\frac{(5^{\frac{2}{3}}-1)*5^{\frac{2}{3}}}{5^{\frac{1}{3}}*5^{\frac{2}{3}}}\\\\=\frac{5^{\frac{4}{3}}-5^{\frac{2}{3}}}{5}$