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Rewrite the expression with rational exponents. \( \sqrt[3]{18} \) \( \sqrt[3]{18}=\square \)

Ask by Johnston Norton. in the United States
Mar 11,2025

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Answer

\[ \sqrt[3]{18} = 18^{\frac{1}{3}} \]

Solution

To rewrite the expression \( \sqrt[3]{18} \) with rational exponents, we can use the property that the \( n \)-th root of a number can be expressed as that number raised to the power of \( \frac{1}{n} \). In this case, the cube root can be expressed as: \[ \sqrt[3]{18} = 18^{\frac{1}{3}} \] Thus, we have: \[ \sqrt[3]{18} = 18^{\frac{1}{3}} \] So, the final answer is: \[ \sqrt[3]{18} = 18^{\frac{1}{3}} \]

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Mind Expander

\( \sqrt[3]{18} = 18^{1/3} \) This means that you take the number 18 and raise it to the power of one-third! It’s like saying, “What number multiplied by itself three times gives you 18?” A fun twist in exponents!

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