Which is equivalent to 4sqrt9^1/2x

sqrt9^1/2x is subject to misinterpretation and should be clarified through the insertion of parentheses. Did you mean sqrt (9^ (x/2)) ? or sqrt (9^ (1/2x)) ?

I will take a chance and assume that you meant 4sqrt (9^ (x/2)). Rewriting this, we get

4 (9^ (x/2)) ^ (1/2)

The coefficient 4 does not change.

But (9^ (x/2)) ^ (1/2) be3comes 9^[ (x/2) * (1/2), so that we now have

4*9^[ (x/2) * (1/2) = 4*9^ (x/4).

4*9^ (1/4) = 4 * (3^2) ^ (1/4) = 4 * (3) ^ (2/4) = 4 * (3) ^ (1/2)

You could leave this result as is, or rewrite it as 4sqrt (3).