Rational Exponents

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What is a rational exponent?

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@@x^{rac{3}{2}} = rac{ ext{sqrt}(x^3)}{1} = ext{sqrt}(x^3)$$.

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What is the relationship between rational exponents and roots?

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@@x^{rac{5}{4}} = ext{sqrt[4]{x^5}} = rac{x^{5/4}}{1}$$.

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@@x^{-rac{3}{2}} = rac{1}{x^{rac{3}{2}}} = rac{1}{ ext{sqrt}(x^3)}$$.

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@@2^{rac{3}{5}} = ext{root}(2^3, 5) = ext{root}(8, 5)$$.

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@@4^{rac{1}{2}} = ext{sqrt}(4) = 2$$.

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@@8^{rac{2}{3}} = ext{root}(8^2, 3) = ext{root}(64, 3)$$.

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@@x^{rac{2}{3}} = ext{root}(x^2, 3) = ext{root}(x^2)$$.

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@@x^{-rac{4}{5}} = rac{1}{x^{rac{4}{5}}} = rac{1}{ ext{root}(x^4, 5)}$$.