Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{{(\frac{1}{2})}^{2}}+{(\frac{2}{3})}^{-2}-{(\frac{3}{4})}^{-2}weget\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{\frac{1}{{2}^{2}}}+{(\frac{2}{3})}^{-2}-{(\frac{3}{4})}^{-2}weget\]
Simplify \({2}^{2}\) to \(4\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{\frac{1}{4}}+{(\frac{2}{3})}^{-2}-{(\frac{3}{4})}^{-2}weget\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{\frac{1}{4}}+\frac{1}{{(\frac{2}{3})}^{2}}-{(\frac{3}{4})}^{-2}weget\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{\frac{1}{4}}+\frac{1}{\frac{{2}^{2}}{{3}^{2}}}-{(\frac{3}{4})}^{-2}weget\]
Simplify \({2}^{2}\) to \(4\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{\frac{1}{4}}+\frac{1}{\frac{4}{{3}^{2}}}-{(\frac{3}{4})}^{-2}weget\]
Simplify \({3}^{2}\) to \(9\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{\frac{1}{4}}+\frac{1}{\frac{4}{9}}-{(\frac{3}{4})}^{-2}weget\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{\frac{1}{4}}+\frac{1}{\frac{4}{9}}-\frac{1}{{(\frac{3}{4})}^{2}}weget\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{\frac{1}{4}}+\frac{1}{\frac{4}{9}}-\frac{1}{\frac{{3}^{2}}{{4}^{2}}}weget\]
Simplify \({3}^{2}\) to \(9\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{\frac{1}{4}}+\frac{1}{\frac{4}{9}}-\frac{1}{\frac{9}{{4}^{2}}}weget\]
Simplify \({4}^{2}\) to \(16\).
\[Ons\imath mpl\imath fy\imath ng\times \frac{1}{\frac{1}{4}}+\frac{1}{\frac{4}{9}}-\frac{1}{\frac{9}{16}}weget\]
Invert and multiply.
\[Ons\imath mpl\imath fy\imath ng\times 1\times 4+\frac{1}{\frac{4}{9}}-\frac{1}{\frac{9}{16}}weget\]
Simplify \(Ons\imath mpl\imath fy\imath ng\times 1\times 4\) to \(4smplfyngOn\imath \imath \imath \).
\[4smplfyngOn\imath \imath \imath +\frac{1}{\frac{4}{9}}-\frac{1}{\frac{9}{16}}weget\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[4smplfyngOn{\imath }^{3}+\frac{1}{\frac{4}{9}}-\frac{1}{\frac{9}{16}}weget\]
Isolate \({\imath }^{2}\).
\[4smplfyngOn{\imath }^{2}\imath +\frac{1}{\frac{4}{9}}-\frac{1}{\frac{9}{16}}weget\]
Use Square Rule: \({i}^{2}=-1\).
\[4smplfyngOn\times -1\times \imath +\frac{1}{\frac{4}{9}}-\frac{1}{\frac{9}{16}}weget\]
Simplify \(4smplfyngOn\times -1\times \imath \) to \(-4smplfyngOn\imath \).
\[-4smplfyngOn\imath +\frac{1}{\frac{4}{9}}-\frac{1}{\frac{9}{16}}weget\]
Regroup terms.
\[-4On\imath smplfyng+\frac{1}{\frac{4}{9}}-\frac{1}{\frac{9}{16}}weget\]
Invert and multiply.
\[-4On\imath smplfyng+\frac{9}{4}-\frac{1}{\frac{9}{16}}weget\]
Invert and multiply.
\[-4On\imath smplfyng+\frac{9}{4}-\frac{16}{9}weget\]
Simplify \(\frac{16}{9}weget\) to \(\frac{16weget}{9}\).
\[-4On\imath smplfyng+\frac{9}{4}-\frac{16weget}{9}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[-4On\imath smplfyng+\frac{9}{4}-\frac{16w{e}^{2}gt}{9}\]
Regroup terms.
\[-4On\imath smplfyng+\frac{9}{4}-\frac{16{e}^{2}wgt}{9}\]
-4*On*IM*s*m*p*l*f*y*n*g+9/4-(16*e^2*w*g*t)/9
