To solve the expressions and round them to the nearest thousandth, follow these steps:
1. Evaluate the expression [tex]\( 3.2^{1.5} \)[/tex]:
- Calculate [tex]\( 3.2^{1.5} \)[/tex].
- The value of this expression is approximately [tex]\( 5.7243340223994625 \)[/tex].
- Round this result to the nearest thousandth. The rounded value is [tex]\( 5.724 \)[/tex].
Therefore,
[tex]\( 3.2^{1.5} \approx 5.724 \)[/tex].
2. Evaluate the expression [tex]\( \left(\frac{3}{5}\right)^{-0.85} \)[/tex]:
- Calculate [tex]\( \left( \frac{3}{5} \right)^{-0.85} \)[/tex].
- The value of this expression is approximately [tex]\( 1.5437303309085206 \)[/tex].
- Round this result to the nearest thousandth. The rounded value is [tex]\( 1.544 \)[/tex].
Therefore,
[tex]\(\left(\frac{3}{5}\right)^{-0.85} \approx 1.544\)[/tex].
So, the solutions to the given expressions rounded to the nearest thousandth are:
[tex]\[
3.2^{1.5} \approx 5.724
\][/tex]
[tex]\[
\left(\frac{3}{5}\right)^{-0.85} \approx 1.544
\][/tex]
