Pregunta
Find the cube root. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \sqrt[3]{\mathrm{x}^{36}}=\square \) B. The cube root is not a real number. Bof 1 A
Ask by Allan Elliott. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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A. \( \sqrt[3]{\mathrm{x}^{36}} = \mathrm{x}^{12} \)
Solución
To find the cube root of \( \mathrm{x}^{36} \), we can use the property of exponents that states:
\[
\sqrt[3]{a^b} = a^{\frac{b}{3}}
\]
Applying this to our expression:
\[
\sqrt[3]{\mathrm{x}^{36}} = \mathrm{x}^{\frac{36}{3}} = \mathrm{x}^{12}
\]
Thus, the correct choice is:
A. \( \sqrt[3]{\mathrm{x}^{36}} = \mathrm{x}^{12} \)
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Simplifique esta solución The Deep Dive
The cube root of \( \mathrm{x}^{36} \) can be found by using the property of exponents. Since the cube root is the same as raising to the power of \( \frac{1}{3} \), we can write it as \( \mathrm{x}^{36 \cdot \frac{1}{3}} = \mathrm{x}^{12} \). So the correct choice is: A. \( \sqrt[3]{\mathrm{x}^{36}} = \mathrm{x}^{12} \). Remember, every real number has a real cube root, so \( B \) would not be applicable here.
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