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Lesson

Notes

Rational Exponent Form & Radical Form

\(\displaystyle x^{a/b} = \sqrt[b]{x^a} = \left(\sqrt[b]{x}\right)^a\)

Practice Problems & Videos

\(\textbf{1)}\) Express \(\sqrt[3]{x^2}\) in Rational Exponent Form

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The answer is \(\displaystyle x^{2/3}\)

\(\textbf{2)}\) Express \(\sqrt[5]{2^3}\) in Rational Exponent Form

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The answer is \(\displaystyle 2^{3/5}\)

\(\textbf{3)}\) Express \(\sqrt[4]{3.1^7}\) in Rational Exponent Form

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The answer is \(\displaystyle 3.1^{7/4}\)

\(\textbf{4)}\) Express \(\sqrt[5]{x^3}\) in Rational Exponent Form

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The answer is \(\displaystyle x^{3/5}\)

\(\textbf{5)}\) Express \(\displaystyle z^{1/7}\) in Radical Form

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The answer is \(\sqrt[7]{z}\)

\(\textbf{6)}\) Express \(\displaystyle 5^{5/2}\) in Radical Form

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The answer is \(\sqrt{5^5}\) or \(\left(\sqrt{5}\right)^5\)

\(\textbf{7)}\) Express \(\displaystyle 4.2^{3/4}\) in Radical Form

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The answer is \(\sqrt[4]{4.2^3}\) or \(\left(\sqrt[4]{4.2}\right)^3\)

\(\textbf{8)}\) Express \(\displaystyle x^{1/4}\) in Radical Form

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The answer is \(\sqrt[4]{x}\)

\(\textbf{9)}\) Express \(\displaystyle x^{2/3}\) in Radical Form

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The answer is \(\sqrt[3]{x^2}\) or \(\left(\sqrt[3]{x}\right)^2\)

\(\textbf{10)}\) Express \(\displaystyle 3^{4/5}\) in Radical Form

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The answer is \(\sqrt[5]{3^4}\) or \(\left(\sqrt[5]{3}\right)^4\)

See Related Pages\(\)

\(\bullet\text{ Intro to Exponents}\)
\(\,\,\,\,\,\,\,\,3^2=3 \times 3 =9\)

\(\bullet\text{ Negative Exponents}\)
\(\,\,\,\,\,\,\,\,3^{-2}=\frac{1}{9}\)

\(\bullet\text{ Rational Exponents}\)
\(\,\,\,\,\,\,\,\,\displaystyle x^{a/b}=\sqrt[b]{x^a}\)

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