Answer
$\frac{2\sqrt2}{3c}$
Work Step by Step
$\frac{4}{\sqrt{18c^2}}\longrightarrow$ factor out perfect squares
=$\frac{4}{\sqrt{9c^2\times2}}\longrightarrow$ multiplication property of square roots
=$\frac{4}{\sqrt{9c^2}\times\sqrt2}\longrightarrow$ simplify
=$\frac{4}{3c\sqrt2}\longrightarrow$ multiply the numerator and denominator by $\sqrt2$
=$\frac{4}{3c\sqrt2}\times\frac{\sqrt2}{\sqrt2}\longrightarrow$ multiply
=$\frac{4\sqrt2}{6c}\longrightarrow$ simplify
=$\frac{2\sqrt2}{3c}$
