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[(a^(1/2) b⁻¹)/(a⁻³ b^(1/3)]^(1/2)
= [(a^(1/2 - (-3)) b^(-1 - 1/3))]^(1/2)
= [a^(7/2) b^(-4/3)]^(1/2)
= a^(7/4) b^(-2/3)