Question

use technology to evaluate the expression.
$left(\frac{3}{8}\
ight)^{\frac{5}{11}}$
$left(\frac{3}{8}\
ight)^{\frac{5}{11}} \approx \square$
(type an integer or decimal rounded to the nearest thousandth as needed.)

Explanation:

Step1: Use calculator

Input \((\frac{3}{8})^{\frac{5}{11}}\) into calculator.

Step2: Calculate

\((\frac{3}{8})^{\frac{5}{11}}=\exp(\frac{5}{11}\ln(\frac{3}{8}))\). First, \(\ln(\frac{3}{8})=\ln3 - \ln8\approx1.0986 - 2.0794=- 0.9808\). Then \(\frac{5}{11}\times(-0.9808)\approx - 0.4458\). And \(\exp(-0.4458)\approx0.640\)

Answer:

\(0.640\)