Rational Exponents and Radical Expressions

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What is a rational exponent?

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@@ ext{The radical form is } \, \sqrt{x}.$$

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What is the relationship between rational exponents and radical expressions?

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@@ ext{This can be rewritten as } a^{-rac{1}{3}}.$$

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@@ ext{The radical form is } \sqrt[4]{x^3}.$$

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@@ ext{Using the laws of exponents, this simplifies to } x^{rac{3}{2} - rac{1}{2}} = x^{1} = x.$$

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@@ ext{The radical form is } \frac{1}{7^2}.$$

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@@ ext{This equals } \sqrt[3]{8^2} = \sqrt[3]{64} = 4.$$

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@@ ext{This can be rewritten as } x^{-rac{3}{4}}.$$

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@@ ext{The radical form is } \frac{1}{\sqrt{x}}.$$