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\left(\frac{3}{2^{2}}\right)^{2}
Cancel out 2^{4}\times 3^{3} in both numerator and denominator.
\left(\frac{3}{4}\right)^{2}
Calculate 2 to the power of 2 and get 4.
\frac{9}{16}
Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.