Let's solve each expression step-by-step.
First, let's work on the expression [tex]\((-2)^3 + 10^0 + 8^1 + 0^3 + 6^3\)[/tex]:
1. Calculate [tex]\((-2)^3\)[/tex]:
[tex]\[
(-2)^3 = -2 \times -2 \times -2 = -8
\][/tex]
2. Calculate [tex]\(10^0\)[/tex]:
[tex]\[
10^0 = 1
\][/tex]
3. Calculate [tex]\(8^1\)[/tex]:
[tex]\[
8^1 = 8
\][/tex]
4. Calculate [tex]\(0^3\)[/tex]:
[tex]\[
0^3 = 0
\][/tex]
5. Calculate [tex]\(6^3\)[/tex]:
[tex]\[
6^3 = 6 \times 6 \times 6 = 216
\][/tex]
Next, add all the terms together:
[tex]\[
(-8) + 1 + 8 + 0 + 216 = 217
\][/tex]
So, the value of the first expression is:
[tex]\[
(-2)^3 + 10^0 + 8^1 + 0^3 + 6^3 = 217
\][/tex]
Now, let's work on the expression [tex]\(3^{-2} + 6^{-1}\)[/tex]:
1. Calculate [tex]\(3^{-2}\)[/tex]:
[tex]\[
3^{-2} = \frac{1}{3^2} = \frac{1}{9} \approx 0.1111
\][/tex]
2. Calculate [tex]\(6^{-1}\)[/tex]:
[tex]\[
6^{-1} = \frac{1}{6} \approx 0.1667
\][/tex]
Next, add these terms together:
[tex]\[
0.1111 + 0.1667 = 0.2778
\][/tex]
So, the value of the second expression is:
[tex]\[
3^{-2} + 6^{-1} \approx 0.2778
\][/tex]
Therefore, our final results are:
[tex]\[
(-2)^3 + 10^0 + 8^1 + 0^3 + 6^3 = 217
\][/tex]
[tex]\[
3^{-2} + 6^{-1} \approx 0.2778
\][/tex]
