Pregunta
Write the rational exponent as a radical expression. \( \begin{array}{ll}(E x l) \\ \text { a. } 7^{\frac{1}{7}} & \text { b. } 4^{\frac{5}{3}}\end{array} \)
Ask by Bradley Fleming. in the United States
Mar 19,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( 7^{\frac{1}{7}} = \sqrt[7]{7} \) and \( 4^{\frac{5}{3}} = \sqrt[3]{4^5} \).
Solución
1. For \( 7^{\frac{1}{7}} \):
- The exponent \(\frac{1}{7}\) indicates a seventh root.
- Thus, \( 7^{\frac{1}{7}} = \sqrt[7]{7} \).
2. For \( 4^{\frac{5}{3}} \):
- The exponent \(\frac{5}{3}\) can be interpreted as \(4^{\frac{5}{3}} = \left(4^5\right)^{\frac{1}{3}}\) or equivalently as \(\left( \sqrt[3]{4} \right)^5\).
- Therefore, \( 4^{\frac{5}{3}} = \sqrt[3]{4^5} \).
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Simplifique esta solución The Deep Dive
Sure! Here are the radical expressions for the given rational exponents: For \( 7^{\frac{1}{7}} \), you can express it as \( \sqrt[7]{7} \). This means you take the seventh root of 7, which is like having a special key to unlock a number! For \( 4^{\frac{5}{3}} \), you can rewrite it as \( \sqrt[3]{4^5} \) or \( \left( \sqrt[3]{4} \right)^5 \). That’s taking the cube root of 4 and then raising it to the fifth power—it's a double workout for your math skills!
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