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Use radical notation to write the expression. Simplify if possible. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. \( (-125)^{\frac{2}{3}} \) \( ( \) Simplify your answer. Type an exact answer, using radicals as needed.) B. The answer is not a real number.

Ask by Murray Nichols. in the United States
Mar 15,2025

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The expression \( (-125)^{\frac{2}{3}} \) simplifies to 25.

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To express \( (-125)^{\frac{2}{3}} \) in radical notation, we can break it down. The expression involves taking the cube root and then squaring. Therefore, it can be rewritten as \( \left(\sqrt[3]{-125}\right)^2 \). The cube root of \(-125\) is \(-5\) because \(-5 \times -5 \times -5 = -125\). Now, squaring \(-5\) gives us \(25\). So the simplified answer is \( 25 \). It looks like option A is the right choice since we have a real number and the answer is: A. \( 25 \)

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