4.0-4.2 Review

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What is the fourth root of a variable raised to a power?

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The fourth root of a variable raised to a power is expressed as @@ ext{If } k^n, ext{ then } ext{the fourth root is } ext{ } oot{4}{k^n} = k^{rac{n}{4}}@@.

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To simplify, use the properties of exponents: @@rac{ oot{3}{x^{18}}}{ oot{2}{x^4}} = rac{x^{rac{18}{3}}}{x^{rac{4}{2}}} = rac{x^6}{x^2} = x^{6-2} = x^4@@.

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What is the process to rewrite an expression in radical form?

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To rewrite an expression in radical form, identify the exponent and convert it using the radical notation: @@x^{rac{m}{n}} = oot{n}{x^m}@@.

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How do you express a radical in exponential form?

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A radical can be expressed in exponential form by converting the root to a fractional exponent: @@ oot{n}{x} = x^{rac{1}{n}}@@.

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What is the rule for dividing exponents with the same base?

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What is the definition of a radical expression?

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A radical expression is an expression that includes a root, such as a square root or cube root, represented as @@ oot{n}{x}@@.

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What is the relationship between exponents and roots?

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Exponents and roots are inversely related: @@ oot{n}{x^m} = x^{rac{m}{n}}@@.

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Convert to radical form: @@x^{rac{1}{2}} = oot{2}{x}@@.

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What is the simplified form of @@rac{ oot{3}{x^{18}}}{ oot{2}{x^4}}@@?

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