Let's solve the given expression step-by-step:
### Expression
[tex]\[
\left(\frac{2^{-1}}{2-4}\right)^0-\frac{5}{8}-\frac{4}{5}+\left(\frac{2}{3}\right)(5-1)+8-(9-1)
\][/tex]
### Step-by-Step Solution
1. Calculate [tex]\(\frac{2^{-1}}{2-4}\)[/tex]:
[tex]\[
2^{-1} = \frac{1}{2}
\][/tex]
[tex]\[
2 - 4 = -2
\][/tex]
[tex]\[
\frac{\frac{1}{2}}{-2} = \frac{1}{2} \times -\frac{1}{2} = -\frac{1}{4} = -0.25
\][/tex]
2. Evaluate [tex]\(\left(-0.25\right)^0\)[/tex]:
Any non-zero number raised to the power of 0 is 1.
[tex]\[
\left(-0.25\right)^0 = 1
\][/tex]
3. Evaluate [tex]\(-\frac{5}{8}\)[/tex]:
[tex]\[
-\frac{5}{8} = -0.625
\][/tex]
4. Evaluate [tex]\(-\frac{4}{5}\)[/tex]:
[tex]\[
-\frac{4}{5} = -0.8
\][/tex]
5. Calculate [tex]\(\left(\frac{2}{3}\right)(5-1)\)[/tex]:
[tex]\[
5 - 1 = 4
\][/tex]
[tex]\[
\left(\frac{2}{3}\right) \times 4 = \frac{2 \times 4}{3} = \frac{8}{3} \approx 2.67
\][/tex]
6. Simplify [tex]\(8\)[/tex]:
[tex]\[
8
\][/tex]
7. Evaluate [tex]\(-(9-1)\)[/tex]:
[tex]\[
9 - 1 = 8
\][/tex]
[tex]\[
-(8) = -8
\][/tex]
8. Summing up all the calculated terms:
[tex]\[
1 - 0.625 - 0.8 + 2.67 + 8 - 8
\][/tex]
Let's add them in sequence:
[tex]\[
1 - 0.625 = 0.375
\][/tex]
[tex]\[
0.375 - 0.8 = -0.425
\][/tex]
[tex]\[
-0.425 + 2.67 = 2.245
\][/tex]
[tex]\[
2.245 + 8 = 10.245
\][/tex]
[tex]\[
10.245 - 8 = 2.245
\][/tex]
Therefore, the final result of the given expression is:
[tex]\[
\boxed{2.241666666666667}
\][/tex]
