Answer
$4.3^{1/2}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{4.3^{-1/5}}{4.3^{-7/10}}
,$ simplifies to
\begin{array}{l}\require{cancel}
4.3^{-\frac{1}{5}-\left( -\frac{7}{10} \right)}
\\\\=
4.3^{-\frac{1}{5}+\frac{7}{10}}
\\\\=
4.3^{-\frac{2}{10}+\frac{7}{10}}
\\\\=
4.3^{\frac{5}{10}}
\\\\=
4.3^{\frac{1}{2}}
\\\\=
4.3^{1/2}
.\end{array}