Radicals and Rational Exponents

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What is a radical?

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A radical is an expression that includes a root, such as a square root or cube root. For example, @@ ext{radical } ext{of } 4 = ext{ } oot{2}{4} = 2@@.

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What does it mean to rewrite a radical in exponential form?

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Rewriting a radical in exponential form involves expressing the root as a fractional exponent. For example, @@ oot{n}{a} = a^{rac{1}{n}}@@.

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When rewriting a radical in exponential form, where does the power go in the fraction?

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The power goes on the numerator of the fraction.

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@@4^{rac{3}{2}} = ext{ } oot{2}{4}^3 = ext{ } oot{2}{4} imes oot{2}{4} imes oot{2}{4}@@.

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What is the exponential form of @@ oot{3}{x}^5@@?

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@@12^{rac{3}{4}} = ext{ } oot{4}{12}^3@@.

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What is the exponential form of @@ oot{2}{x}@@?

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Front

What is the relationship between radicals and rational exponents?

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Radicals can be expressed as rational exponents, where the root is the denominator and the power is the numerator.

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How do you convert @@ oot{n}{a}@@ to exponential form?

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To convert, use the formula @@ oot{n}{a} = a^{rac{1}{n}}@@.

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What is the value of @@ oot{2}{16}@@?

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