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A. \(\frac{{{a^\alpha }}}{{{a^\beta }}} = {a^{\frac{\alpha }{\beta }}}\)

B. \({a^{\sqrt \alpha  }} = {\left( {\sqrt a } \right)^\alpha }\left( {\alpha  > 0} \right).\)

C. \({a^{{\alpha ^\beta }}} = {\left( {{a^\alpha }} \right)^\beta }\)

D. \(\sqrt {{a^\alpha }}  = {\left( {\sqrt a } \right)^\alpha }\)