Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\sqrt{\frac{{3}^{2}}{{2}^{2}}-4}\times \frac{-1}{2}\]
Simplify \({3}^{2}\) to \(9\).
\[\sqrt{\frac{9}{{2}^{2}}-4}\times \frac{-1}{2}\]
Simplify \({2}^{2}\) to \(4\).
\[\sqrt{\frac{9}{4}-4}\times \frac{-1}{2}\]
Simplify \(\frac{9}{4}-4\) to \(-\frac{7}{4}\).
\[\sqrt{-\frac{7}{4}}\times \frac{-1}{2}\]
Simplify \(\sqrt{-\frac{7}{4}}\) to \(\sqrt{\frac{7}{4}}\imath \).
\[\sqrt{\frac{7}{4}}\imath \times \frac{-1}{2}\]
Simplify \(\sqrt{\frac{7}{4}}\) to \(\frac{\sqrt{7}}{\sqrt{4}}\).
\[\frac{\sqrt{7}}{\sqrt{4}}\imath \times \frac{-1}{2}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[\frac{\sqrt{7}}{2}\imath \times \frac{-1}{2}\]
Simplify.
\[\frac{-\sqrt{7}\imath }{4}\]
Move the negative sign to the left.
\[-\frac{\sqrt{7}\imath }{4}\]
-(sqrt(7)*IM)/4
