A very large number x is equal to \(2^23^34^45^56^67^78^89^9\). What is the smallest positive integer that, when multiplied with x, produces a product that is a perfect square?

Thank You So Much!!!

Hint: All the indices must be even numbers.

Except 9^9 = 3^18

Yes you are right,

I will tweak my answer.

All the factors must be prime THEN all the indices of these prme factors must by even.

So with your example.

\(9^9=(3^2)^9=3^{18}\\ \text{18 is even so } 9^9 \text { is a square number}\)