Answer:
n^10/(144m^4)
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
(ab)^c = (a^c)(b^c)
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Using these rules, we can simplify the given expression as follows:
[tex]\left(\dfrac{3m^{-5}n^2}{4m^{-2}n^0}\right)^2\left(\dfrac{mn^4}{9n}\right)^2=\left(\dfrac{3}{4}m^{-5(-(-2))}n^{2-0}\right)^2\left(\dfrac{1}{9}mn^{4-1}\right)^2\\\\=\left(\dfrac{3n^2}{4m^3}\right)^2\left(\dfrac{m^3}{9}\right)^2=\dfrac{3^2n^4}{4^2m^6}\cdot\dfrac{m^2n^6}{9^2}=\boxed{\dfrac{n^{10}}{144m^4}}[/tex]
