Answer:
p^(2(s-t)^2)/(s+t)
Explanation:
We can simplify this expression by using the properties of exponents:
((p^r)/(p^s))^(r+s) ((p^2)/(p^t))^(s+t) ((p^t)/(p^r))^(r+t)
= (p^(r+s-s))^r (p^(2s-2t))^s (p^(t-r+r))^t / (p^(r+s-r))^r (p^(2t-2s))^s (p^(r-t+t))^t
= p^r p^(2s-2t)s p^t / p^r p^(2t-2s)s p^t
= p^r / p^r * (p^(2s-2t))^(s/(s+t)) / (p^(2t-2s))^(s/(s+t))
= p^r / p^r * p^((2s-2t)s/(s+t)) / p^((2t-2s)s/(s+t))
= p^0 * p^(2s^2-2st-2ts+2t^2)/(s+t)
= p^(2s^2-2st-2ts+2t^2)/(s+t)
= p^(2(s-t)^2)/(s+t)
Therefore, ((p^r)/(p^s))^(r+s) ((p^2)/(p^t))^(s+t) ((p^t)/(p^r))^(r+t) simplifies to p^(2(s-t)^2)/(s+t).