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If $$a = \sqrt[3]{4}, b = \sqrt[4]{5}, c = \sqrt[4]{7}$$ and $$d = \sqrt[3]{9}$$, then their correct ordering is
a = $$\sqrt[\ 3]{4}\ =\ \sqrt[\ 12]{256}$$
b = $$\sqrt[\ 4]{5}\ =\ \sqrt[\ 12]{125}$$
c = $$\sqrt[\ 4]{7}\ =\ \sqrt[\ 12]{343}$$
d=$$\sqrt[\ 3]{9}\ =\ \sqrt[\ 12]{6561}$$
hence b<a<c<d
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