Pregunta
Use radical notation to write the expression. Simplify if possible. \( (-8)^{\frac{1}{3}} \) Select the correct choice below and fill in any answer boxes in your choice. A. \( (-8)^{\frac{1}{3}}=\square \) Points: 0 of 1 (Simplify your answer. Type an exact answer, using radicals as needed.) B. The answer is not a real number.
Ask by Nichols Parry. in the United States
Mar 15,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\[
(-8)^{\frac{1}{3}} = -2
\]
Solución
We need to find the cube root of \(-8\). In radical notation, this is written as:
\[
\sqrt[3]{-8}
\]
Since the cube root is an odd root, we can compute:
\[
\sqrt[3]{-8} = -\sqrt[3]{8} = -2
\]
Thus, the simplified expression is:
\[
(-8)^{\frac{1}{3}} = -2
\]
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Bonus Knowledge
A. \( (-8)^{\frac{1}{3}}= -2 \) To simplify, we recognize that raising -8 to the power of \( \frac{1}{3} \) means we're finding the cube root of -8. Since -2 multiplied by itself three times gives -8, the simplest form of this expression is indeed -2. Feeling a little adventurous with cube roots? They can be a lot of fun. Unlike square roots, which must be non-negative when dealing with real numbers, cube roots open the door for negative numbers to play along. So when you see \( (-8)^{\frac{1}{3}} \), you're tapping into that cube-root magic!

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