Question

use the aleks calculator to evaluate each expression. round your answers to the nearest thousandth. do not round any intermediate computations.
$3.2^{1.5}=\square$
$left(\frac{5}{7}\
ight)^{-0.65}=\square$

Explanation:

Step1: Calculate \(3.2^{1.5}\)

Using a calculator, \(3.2^{1.5}=3.2^{\frac{3}{2}}=\sqrt{3.2^{3}}=\sqrt{32.768}\approx5.724\)

Step2: Calculate \((\frac{5}{7})^{- 0.65}\)

Using the property \(a^{-n}=\frac{1}{a^{n}}\), \((\frac{5}{7})^{-0.65}=(\frac{7}{5})^{0.65}\). Using a calculator, \((\frac{7}{5})^{0.65}\approx1.273\)

Answer:

\(3.2^{1.5}\approx5.724\)
\((\frac{5}{7})^{-0.65}\approx1.273\)