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Answer:
(c) 1/(36·a^4·b^10)
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
(a^b)^c = a^(bc)
a^-1 = 1/a
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[tex]\left(\dfrac{(2a^{-3}b^4)^2}{(3a^5b)^{-2}}\right)^{-1}=\dfrac{(3a^5b)^{-2}}{(2a^{-3}b^4)^2}=\dfrac{3^{-2}a^{-10}b^{-2}}{2^2a^{-6}b^8}=\dfrac{1}{3^22^2}a^{-10-(-6)}b^{-2-8}\\\\=\boxed{\dfrac{1}{36a^4b^{10}}}[/tex]
