(2x^sqrt of 2x)(3^sqrt of 5x)
To simplify the expression (2x^sqrt(2x))(3^sqrt(5x)), we can follow the rules of exponents.
First, let's simplify the expression within each parenthesis separately.
In the first parenthesis, we have 2x^sqrt(2x). Note that sqrt(2x) can be rewritten as (2x)^(1/2). Therefore, we have:
2x^(sqrt(2x)) = 2x^(2x)^(1/2) = 2(x^(2x))^(1/2).
Now, let's move on to the second parenthesis. We have 3^sqrt(5x), which can be rewritten as (5x)^(1/2). Therefore, we have:
3^sqrt(5x) = 3^(5x)^(1/2) = (3^(5x))^(1/2).
Now, let's put everything together:
(2x^sqrt(2x))(3^sqrt(5x)) = 2(x^(2x))^(1/2) * (3^(5x))^(1/2).
Using the laws of exponents, we can simplify further:
2(x^(2x))^(1/2) * (3^(5x))^(1/2) = 2 * (x^(2x) * 3^(5x))^(1/2).
In this form, we have simplified the expression as much as possible.