Simplified value of 125^2/3x√25x3√5^3x5^1/2

To simplify the expression 125^2/3x√25x3√5^3x5^1/2, we will break it down step by step.

Step 1: Simplify the exponents
First, let's simplify the exponents in the expression.

125^(2/3) can be simplified as the cube root of 125 squared.
125^(2/3) = (cube root of 125)^2 = 5^2 = 25

Next, let's simplify the exponents in the expression 5^3 and 5^1/2.
5^3 = 5 x 5 x 5 = 125
5^1/2 = square root of 5

Now our expression becomes:
25 x √25 x 3√125 x √5

Step 2: Simplify the square roots
Let's simplify the square roots in the expression.

√25 = 5

Now our expression becomes:
25 x 5 x 3√125 x √5

Step 3: Simplify the cube root
Let's simplify the cube root in the expression.

3√125 = cube root of 125 = 5

Now our expression becomes:
25 x 5 x 5 x √5

Step 4: Multiply the remaining terms
Finally, let's multiply the remaining terms in the expression.

25 x 5 x 5 x √5 = 625 x √5

Therefore, the simplified value of 125^2/3x√25x3√5^3x5^1/2 is 625√5.