Can somebody show me how to do this problem? (5^ square root of 5x^2 y)^11.

Certainly! To simplify this expression, we can follow these steps:

Step 1: Recognize the components of the expression.
The expression consists of a base (5), an exponent (the square root of 5x^2y), and a final exponent (11).

Step 2: Simplify the exponent.
To simplify an exponent with a square root, we can multiply the inner exponent by the square root outside the parentheses. In this case, the square root of 5x^2y is the inner exponent. Therefore, we can multiply it by the square root outside the parentheses, which is sqrt(5):
(sqrt(5x^2y))^11 becomes (5x^2y)^(11/2)

Step 3: Apply the exponent to the base.
Now, consider the base (5) raised to the simplified exponent (11/2):
(5)^(11/2)

Step 4: Evaluate the expression.
To evaluate (5)^(11/2), we can use the exponent rules. In this case, raising a number to a fractional exponent is equivalent to taking the square root of that number raised to the corresponding power. Thus:
(5)^(11/2) = sqrt(5^11)

So, the final simplified expression is sqrt(5^11).