Question

What is the answer to this question

Answer 1

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)

__

Using these rules, we can simplify the given expression as follows:

  $\left(\dfrac{3m^{-5}n^2}{4m^{-2}n^0}\right)^2\left(\dfrac{mn^4}{9n}\right)^2=\left(\dfrac{3}{4}m^{-5(-(-2))}n^{2-0}\right)^2\left(\dfrac{1}{9}mn^{4-1}\right)^2\\\\=\left(\dfrac{3n^2}{4m^3}\right)^2\left(\dfrac{m^3}{9}\right)^2=\dfrac{3^2n^4}{4^2m^6}\cdot\dfrac{m^2n^6}{9^2}=\boxed{\dfrac{n^{10}}{144m^4}}$