Answer:
[tex]\frac{n^4}{144m^4}[/tex]
Step-by-step explanation:
So here we have our equation: [tex](\frac{3m^-^5n^2}{4m^-^2n^0} )^2*(\frac{mn^4}{9n})^2[/tex]
Begin with separating them both and only focusing on [tex](\frac{3m^-^5n^2}{4m^-^2n^0} )^2[/tex] for now. We have the exponent 2 on the outside of the parenthesis which means everything on the inside will be given this exponent, and with variables that have already been given exponents, you simply multiply those exponents together as basic numbers. Our result will be [tex](\frac{3^2m^-^1^0n^4}{4^2m^-^4n^0} )[/tex], now we're going to deal with those negative exponents, when they're negative you need to switch the side of the fraction they're on, say if it's on the bottom and it is negative that variable alone will be transferred to the top, the same goes with if the negative exponent is on the top, it'll basically be brought down to the denominator position. We now have [tex](\frac{3^2n^4m^4}{4^2n^0m^1^0} )[/tex] all that's left is to solve 3^2, 4^2, and n^0 as anything to the power of 0 will always be 1. And we now have our solution for the first segment; [tex](\frac{9n^4m^4}{16m^1^0} )[/tex] :)
Moving on, now focusing on [tex](\frac{mn^4}{9n})^2[/tex] we once again distribute the power of 2 to each variable, which we receive [tex](\frac{m^2n^8}{9^2n^2})[/tex] from. We have no negative exponents so we can skip the part of this process and now move on to factoring 9^2 which is 81 giving us [tex](\frac{m^2n^8}{81n^2})[/tex]!
Our last step is to multiply [tex](\frac{9n^4m^4}{16m^1^0} )[/tex] and [tex](\frac{m^2n^8}{81n^2})[/tex], I'm super sorry but I haven't even personally gotten this far in my lessons so I can't give the answer from myself but I already spent a whole lot of time thinking I'd be able to finish haha, but the result will be [tex]\frac{n^4}{144m^4}[/tex].
