Question
Dound your answers to the nearest thousandth. \( 0.2^{-0.25}= \) \( \left(\frac{2}{7}\right)^{1.4}=\square \)
Ask by Hamilton Mckenzie. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \left(\frac{2}{7}\right)^{1.4} \approx 0.173 \)
Solution
Calculate or simplify the expression \( (2/7)^{1.4} \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(\frac{2}{7}\right)^{1.4}\)
- step1: Convert the expressions:
\(\left(\frac{2}{7}\right)^{\frac{7}{5}}\)
- step2: Use the properties of exponents:
\(\frac{2^{\frac{7}{5}}}{7^{\frac{7}{5}}}\)
- step3: Rewrite the expression:
\(\frac{2^{\frac{7}{5}}}{7\sqrt[5]{7^{2}}}\)
- step4: Rewrite the expression:
\(\frac{2\sqrt[5]{2^{2}}}{7\sqrt[5]{7^{2}}}\)
- step5: Multiply by the Conjugate:
\(\frac{2\sqrt[5]{2^{2}}\times \sqrt[5]{7^{3}}}{7\sqrt[5]{7^{2}}\times \sqrt[5]{7^{3}}}\)
- step6: Simplify:
\(\frac{2\sqrt[5]{2^{2}}\times \sqrt[5]{343}}{7\sqrt[5]{7^{2}}\times \sqrt[5]{7^{3}}}\)
- step7: Multiply the numbers:
\(\frac{2\sqrt[5]{1372}}{7\sqrt[5]{7^{2}}\times \sqrt[5]{7^{3}}}\)
- step8: Multiply the numbers:
\(\frac{2\sqrt[5]{1372}}{49}\)
The value of \( \left(\frac{2}{7}\right)^{1.4} \) is approximately 0.173103.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve these expressions: For \( 0.2^{-0.25} \), we can rewrite it as \( \frac{1}{0.2^{0.25}} \). Calculating \( 0.2^{0.25} \) gives us approximately \( 0.66874 \). Taking the reciprocal, we get \( 0.2^{-0.25} \approx 1.496 \). Rounding to the nearest thousandth, the answer is \( 1.496 \). For \( \left(\frac{2}{7}\right)^{1.4} \), we can first find the value of \( \frac{2}{7} \), which is approximately \( 0.2857 \). Raising this to the power of \( 1.4 \) gives us approximately \( 0.1884 \). Rounding to the nearest thousandth, the answer is \( 0.188 \). So, \( 0.2^{-0.25} \approx 1.496 \) \( \left(\frac{2}{7}\right)^{1.4} \approx 0.188 \)
