Pregunta
Write the expression in exponential form. \[ \sqrt[7]{x^{4}} \]
Ask by Pearson Mathis. in the United States
Jan 25,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\[
x^{\frac{4}{7}}
\]
Solución
To express \(\sqrt[7]{x^{4}}\) in exponential form, you can use the property that the \(n\)th root of a number is the same as raising that number to the power of \(1/n\).
\[
\sqrt[7]{x^{4}} = (x^{4})^{\frac{1}{7}} = x^{\frac{4}{7}}
\]
**Exponential Form:**
\[
x^{\frac{4}{7}}
\]
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Simplifique esta solución Mind Expander
To rewrite the expression \(\sqrt[7]{x^{4}}\) in exponential form, we can express the nth root of a number as a fractional exponent. Thus, \(\sqrt[7]{x^{4}} = x^{4/7}\). This means that you are taking the fourth power of \(x\) and then taking the seventh root of the result, which can also be interpreted as raising \(x\) to the power of \(4/7\). Keep that power fraction handy; it’s a powerful tool in simplifying and solving equations!
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