Answer
$-14r^{\frac{17}{12}}$
Work Step by Step
Using the laws of exponents, the given expression, $
(7r^{1/2})(2r^{3/4})(-r^{1/6})
,$ simplifies to
\begin{array}{l}\require{cancel}
7(2)(-1)r^{\frac{1}{2}+\frac{3}{4}+\frac{1}{6}}
\\\\=
-14r^{\frac{6}{12}+\frac{9}{12}+\frac{2}{12}}
\\\\=
-14r^{\frac{17}{12}}
.\end{array}
