Pregunta
Multiply and leave your answer in radical form. \( \sqrt[5]{x} \cdot \sqrt[6]{x} \)
Ask by Lambert Wright. in the United States
Feb 27,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The product is \( \sqrt[30]{x^{11}} \).
Solución
Calculate or simplify the expression \( \sqrt[5]{x} \cdot \sqrt[6]{x} \).
Simplify the expression by following steps:
- step0: Solution:
\(\sqrt[5]{x}\times \sqrt[6]{x}\)
- step1: Expand the expression:
\(\sqrt[30]{x^{6}}\times \sqrt[30]{x^{5}}\)
- step2: Use the properties of radicals:
\(\sqrt[30]{x^{6}\times x^{5}}\)
- step3: Calculate:
\(\sqrt[30]{x^{11}}\)
The product of \( \sqrt[5]{x} \) and \( \sqrt[6]{x} \) is \( \sqrt[30]{x^{11}} \).
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Simplifique esta solución Extra Insights
To multiply the two expressions \( \sqrt[5]{x} \) and \( \sqrt[6]{x} \), we can rewrite them using exponents. This gives us \( x^{1/5} \cdot x^{1/6} \). When multiplying like bases, we add the exponents. So, we have: \[ x^{1/5 + 1/6} \] To add \( 1/5 \) and \( 1/6 \), we need a common denominator, which is 30. Converting the fractions gives us \( 6/30 + 5/30 = 11/30 \). Thus, we have: \[ x^{11/30} \] Finally, we can express this in radical form: \[ \sqrt[30]{x^{11}} \] So, the final answer is: \[ \sqrt[30]{x^{11}} \]
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