Rational Exponents

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Define rational exponents.

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What is the relationship between rational exponents and radicals?

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Rational exponents and radicals are two ways to express the same mathematical concept. For example, @@x^{rac{m}{n}} = oot{n}{x^m}@@.

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@@x^{rac{3}{4}} = oot{4}{x^3}@@.

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Convert @@ oot{3}{x^5}@@ to a rational exponent.

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@@ oot{3}{x^5} = x^{rac{5}{3}}@@.

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What is @@ oot{5}{x^2}@@ expressed as a rational exponent?

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@@ oot{5}{x^2} = x^{rac{2}{5}}@@.

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Simplify @@ oot{2}{x^8}@@.

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@@ oot{2}{x^8} = x^{4}@@.

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What is the value of @@ oot{3}{x^{12}}@@?

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@@ oot{3}{x^{12}} = x^{4}@@.

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@@x^{rac{9}{2}} = oot{2}{x^9}@@.

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Convert @@ oot{4}{x^6}@@ to a rational exponent.

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@@ oot{4}{x^6} = x^{rac{6}{4}} = x^{rac{3}{2}}@@.