Answer
\( \left(\frac{2}{7}\right)^{1.4} \approx 0.173103 \) and \( 0.3^{-0.35} \approx 1.524079 \).
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:
\(\frac{2\sqrt[5]{1372}}{49}\)
Calculate or simplify the expression \( 0.3^{-0.35} \).
Calculate the value by following steps:
- step0: Calculate:
\(0.3^{-0.35}\)
- step1: Convert the expressions:
\(\left(\frac{3}{10}\right)^{-\frac{7}{20}}\)
- step2: Transform the expression:
\(\left(\frac{10}{3}\right)^{\frac{7}{20}}\)
- step3: Use the properties of exponents:
\(\frac{10^{\frac{7}{20}}}{3^{\frac{7}{20}}}\)
- step4: Rewrite the expression:
\(\frac{10^{\frac{7}{20}}}{\sqrt[20]{3^{7}}}\)
- step5: Rewrite the expression:
\(\frac{\sqrt[20]{10^{7}}}{\sqrt[20]{3^{7}}}\)
- step6: Multiply by the Conjugate:
\(\frac{\sqrt[20]{10^{7}}\times \sqrt[20]{3^{13}}}{\sqrt[20]{3^{7}}\times \sqrt[20]{3^{13}}}\)
- step7: Multiply the numbers:
\(\frac{\sqrt[20]{10^{7}\times 3^{13}}}{\sqrt[20]{3^{7}}\times \sqrt[20]{3^{13}}}\)
- step8: Multiply the numbers:
\(\frac{\sqrt[20]{10^{7}\times 3^{13}}}{3}\)
The results are:
1. \( \left(\frac{2}{7}\right)^{1.4} \approx 0.173103 \)
2. \( 0.3^{-0.35} \approx 1.524079 \)
Answered by UpStudy AI and reviewed by a Professional Tutor
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