Question

What is the answer to this question

Answer 1

n^10/(144m^4)

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:

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