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\[27^{2/3}=\sqrt[3]{27^2}\]\[\sqrt[3]{27^2}=\sqrt[3]{729}\]\[\sqrt[3]{729}=9\]

\[64^{5/6}=\sqrt[5]{64^6}\]\[\sqrt[6]{64^5}=\sqrt[6]{1073741824}\]\[\sqrt[6]{1073741824}=32\]

i am still kind of confused. so for 1^5/3.

\[1^{5/3}=\sqrt[3]{1^5}\]\[\sqrt[3]{1^5}=\sqrt[3]{1}\]\[\sqrt[3]{1}=1\]