((-45)^(2n+1))/((-15)^(2n)*9^n-1)*25

^ - степень

I assume you want me to simplify the expression.

We can start by using the properties of exponents:

((-45)^(2n+1))/((-15)^(2n)*9^n-1)*25^(-k)

= ((-1)^{2n+1} * 3^{2n+1} * 5^{2n+1}) / ((-1)^{2n} * 3^{2n*2} * 3^{-1} * 5^{-k})

= (-3)^{2n+1} * 5^{2n+1} * 5^k / (3^{4n} * 3^{-1} * 5^{-k})

= (-3)^{2n+2} * 5^{3k+1} / 3^{4n+1}

= (-3)^2 * (-3)^{2n} * 5 * 5^k * 5^2 / 3^{4n+1}

= 225 * (-3)^{2n} * 5^{k+2} / 3^{4n+1}

So the simplified expression is 225 * (-3)^{2n} * 5^{k+2} / 3^{4n+1}.