$$\frac{ { \left( \frac{ 4 }{ 16 } \right) }^{ 2 } }{ { \left( \frac{ 8 }{ 32 } \right) }^{ 2 } }$$
$1$
$$\frac{\left(\frac{1}{4}\right)^{2}}{\left(\frac{8}{32}\right)^{2}}$$
$$\frac{\frac{1}{16}}{\left(\frac{8}{32}\right)^{2}}$$
$$\frac{\frac{1}{16}}{\left(\frac{1}{4}\right)^{2}}$$
$$\frac{\frac{1}{16}}{\frac{1}{16}}$$
$$1$$
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