Pregunta
Rewrite the expression \( \sqrt[15]{x^{8}} \) using a rational exponent and no radical sign.
Ask by Byrd Montgomery. in the United States
Jan 27,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( x^{\frac{8}{15}} \)
Solución
To rewrite the expression \( \sqrt[15]{x^{8}} \) using a rational exponent without a radical sign, you can use the property that \(\sqrt[n]{a^m} = a^{\frac{m}{n}}\).
Applying this property:
\[
\sqrt[15]{x^{8}} = x^{\frac{8}{15}}
\]
**Final Answer:**
\[
x^{\,\frac{8}{15}}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Mind Expander
The expression \( \sqrt[15]{x^{8}} \) can be rewritten using a rational exponent as \( x^{\frac{8}{15}} \). This is achieved by recognizing that the nth root of a number can be expressed as that number raised to the power of \( \frac{1}{n} \). In this case, the 15th root corresponds to raising \( x^{8} \) to the power of \( \frac{1}{15} \), which results in \( x^{\frac{8}{15}} \).
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