Pregunta
e) \( 5^{\frac{2}{3}} \div\left(\frac{1}{25}\right)^{-0.2} \)
Ask by Sandoval Ayala. in Canada
Mar 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The result is approximately 1.536.
Solución
Calculate or simplify the expression \( 5^{2/3} / (1/25)^{-0.2} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{5^{\frac{2}{3}}}{\left(\frac{1}{25}\right)^{-0.2}}\)
- step1: Convert the expressions:
\(\frac{5^{\frac{2}{3}}}{\left(\frac{1}{25}\right)^{-\frac{1}{5}}}\)
- step2: Multiply by the reciprocal:
\(5^{\frac{2}{3}}\times \frac{1}{25^{\frac{1}{5}}}\)
- step3: Rewrite the expression:
\(5^{\frac{2}{3}}\times \frac{1}{5^{\frac{2}{5}}}\)
- step4: Reduce the numbers:
\(5^{\frac{4}{15}}\times 1\)
- step5: Simplify:
\(5^{\frac{4}{15}}\)
- step6: Transform the expression:
\(\sqrt[15]{5^{4}}\)
- step7: Simplify:
\(\sqrt[15]{625}\)
The result of \(5^{\frac{2}{3}} \div\left(\frac{1}{25}\right)^{-0.2}\) is approximately 1.536003.
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Simplifique esta solución Mind Expander
First step is to simplify \( 5^{\frac{2}{3}} \). This can be rewritten as \( \sqrt[3]{5^2} = \sqrt[3]{25} \). Now, for the other part, \( \left(\frac{1}{25}\right)^{-0.2} \) can be rewritten as \( 25^{0.2} \) since \( a^{-b} = \frac{1}{a^b} \). Since \( 25 = 5^2 \), we get \( (5^2)^{0.2} = 5^{2 \cdot 0.2} = 5^{0.4} \). So now we’re dealing with \[ \frac{5^{\frac{2}{3}}}{5^{0.4}}. \] Using the property of exponents \( a^m \div a^n = a^{m-n} \): \[ 5^{\frac{2}{3} - 0.4} = 5^{\frac{2}{3} - \frac{4}{10}} = 5^{\frac{2}{3} - \frac{12}{30}} = 5^{\frac{20}{30} - \frac{12}{30}} = 5^{\frac{8}{30}} = 5^{\frac{4}{15}}. \] Thus, the final answer is \( 5^{\frac{4}{15}} \).
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