Answer:
[tex]-\dfrac{4a^{12}b^8}{5}[/tex]
Step-by-step explanation:
The applicable rules of exponents are ...
[tex]\dfrac{1}{a^{-b}}=a^b\\\\a^ba^c=a^{b+c}[/tex]
Your ratio simplifies to ...
[tex]\dfrac{-8a^8b^{-2}}{10a^{-4}b^{-10}}=-\dfrac{4}{5}a^{8-(-4)}b^{-2-(-10)}\\\\=-\dfrac{4a^{12}b^8}{5}[/tex]
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Please note that simplifying the constants, -8/10 to -4/5, eliminates half the answer choices. Since exponents are only multiplied when a power is raised to a power, you can pretty much eliminate the second choice as being unreasonable. ((a^b)^c = a^(bc))
