Dound your answers to the nearest thousandth.

Ask by Hamilton Mckenzie. in the United States

Jan 22,2025

Question

Dound your answers to the nearest thousandth. $$ 0.2^{-0.25}= $$ $$ \left(\frac{2}{7}\right)^{1.4}=\square $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ (2/7)^{1.4} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{2}{7}ight)^{1.4}$$
- step1: Convert the expressions:
  $$\left(\frac{2}{7}ight)^{\frac{7}{5}}$$
- 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:
  $$\frac{2\sqrt[5]{2^{2}}	imes \sqrt[5]{7^{3}}}{7\sqrt[5]{7^{2}}	imes \sqrt[5]{7^{3}}}$$
- step6: Simplify:
  $$\frac{2\sqrt[5]{2^{2}}	imes \sqrt[5]{343}}{7\sqrt[5]{7^{2}}	imes \sqrt[5]{7^{3}}}$$
- step7: Multiply the numbers:
  $$\frac{2\sqrt[5]{1372}}{7\sqrt[5]{7^{2}}	imes \sqrt[5]{7^{3}}}$$
- step8: Multiply the numbers:
  $$\frac{2\sqrt[5]{1372}}{49}$$
The value of $$ \left(\frac{2}{7}ight)^{1.4} $$ is approximately 0.173103.
$$ \left(\frac{2}{7}ight)^{1.4} \approx 0.173 $$

Dound your answers to the nearest thousandth.

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