##(5sqrt5)^2 = 125##

Expressed as ##(5sqrt5)^2##.

Remember that ##a^m xx a^n = a^(m+n)##

Therefore, ##5^(1+1/2) = 5^(3/2)##

Also ##(a^m)^n = a^(mn)##

Hence, ##(5^(3/2))^2 = 5^(3/2 * 2) = 5^3##

##5## to the power of ##3## is ##5*5*5=125.##

Alternatively,

##(5sqrt5)^2 = 5^2 * (sqrt5)^2 = 25 * 5 = 125##