Let's evaluate each expression step-by-step and round the final results to the nearest thousandth.
1. [tex]\(\left(\frac{7}{8}\right)^{18}\)[/tex]:
- First, we need to calculate [tex]\(\left(\frac{7}{8}\right)^{18}\)[/tex].
- This results in approximately [tex]\(0.09039511350064361\)[/tex].
- Rounding this value to the nearest thousandth, we get [tex]\(0.090\)[/tex].
Therefore,
[tex]\[
\left(\frac{7}{8}\right)^{18} \approx 0.090
\][/tex]
2. [tex]\(0.2^{-0.25}\)[/tex]:
- Next, we evaluate [tex]\(0.2^{-0.25}\)[/tex].
- This results in approximately [tex]\(1.4953487812212205\)[/tex].
- Rounding this value to the nearest thousandth, we get [tex]\(1.495\)[/tex].
Therefore,
[tex]\[
0.2^{-0.25} \approx 1.495
\][/tex]
Summarizing the results:
[tex]\[
\left(\frac{7}{8}\right)^{18} \approx 0.090
\][/tex]
[tex]\[
0.2^{-0.25} \approx 1.495
\][/tex]
