Question

Which is equivalent to 4sqrt9^1/2x

Answer 1

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).