We want to see which expression does not belong, the one that has a difference with the others is the third one, so that is the one that does not belong.
Working with exponents.
Here you need to remember the rules:
[tex]a^x*a^y = a^{x + y}\\\\(a^x)^y = a^{x*y}\\\\\frac{a^x}{a^y} = a^{x - y}[/tex]
Now we can use these to rewrite the given expressions as:
[tex]\frac{2^8}{2^5} = 2^{8 - 5} = 2^3 = 8[/tex]
[tex](\frac{3}{4} )^{-5}*(\frac{3}{4})^8 = (\frac{3}{4})^{-5 + 8}= (\frac{3}{4} )^3[/tex]
[tex](4^{-5})^8 = 4^{-5*8} = 4^{-40}[/tex]
[tex]\frac{10^8}{5^5} = \frac{2^8*5^8}{5^5} = (2^8)*(5^{8-5}) = 2^8*5^3[/tex]
So you can see that in the first, second, and fourth expressions we have positive exponents and there always appears the exponent 3, while on the third one that does not happen, so the one that does not belong is the third expression.
If you want to learn more about exponents, you can read:
https://brainly.com/question/11761858
