Fractional Indices

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What is a fractional index?

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How do you multiply terms with the same base?

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@@a^{rac{3}{2}} imes a^{rac{1}{2}} = a^{rac{3}{2} + rac{1}{2}} = a^{rac{4}{2}} = a^2.

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How do you divide terms with the same base?

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@@rac{a^{rac{5}{3}}}{a^{rac{2}{3}}} = a^{rac{5}{3} - rac{2}{3}} = a^{rac{3}{3}} = a^1 = a.

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@@ (a^{rac{1}{3}})^3 = a^{rac{1}{3} imes 3} = a^1 = a.