Rational Exponents and Radical Form

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What is a rational exponent?

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@@ ext{The radical form of } x^{rac{1}{2}} ext{ is } ext{√}x.$$

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What is the relationship between rational exponents and radicals?

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Rational exponents can be expressed as radicals. For example, @@x^{rac{m}{n}} = oot{n}{x^m}@@.

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Convert @@ oot{3}{x^7}@@ to exponential form.

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@@x^{rac{7}{3}}$$.

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@@ oot{4}{x^3}$$.

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Convert @@ oot{4}{(3x)^3}@@ to exponential form.

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@@(3x)^{rac{3}{4}}$$.

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What is the value of @@ oot{2}{x^8}@@ in exponential form?

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@@x^{rac{8}{2}} = x^4$$.

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How do you express @@ oot{5}{(2y^3)}@@ in exponential form?

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@@(2y^3)^{rac{1}{5}}$$.

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@@ oot{2}{x^5}$$.

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Convert @@ oot{3}{(4x^2)}@@ to exponential form.

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@@(4x^2)^{rac{1}{3}}$$.