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Use the ALEKS calculator to evaluate each expression. Round your answers to the nearest thousandth. Do not round any intermediate computations.

[tex]\[
\left(\frac{7}{8}\right)^{18} = \square
\][/tex]

[tex]\[
0.2^{-0.25} = \square
\][/tex]


Sagot :

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]