(5)^-1/2 * (5x)^5/2 (5x)^-3/2 =

1/5*sqrt5x^5(1/sqrt5x^3)=
sqrt5x^5/sqrt5*sqrt5x^3=
x^2 sqrt5x/ sqrt5 * x sqrt5x=
x^2/x sqrt5=
x/sqrt 5

Is this correct? If not, where am I going wrong and what is the answer?

The way it is actually written is

(5)^-1/2 * 5x^5/2 (5x)^-3/2 =

well, 5x^5/2 (5x)^-3/2 = 5x

so, now what do you think?

5x/sqrt5?

I think I understand now. This would be the solution:

(5)^-1/2 * 5x^5/2+(-3/2)=
(5)^-1/2 * 5x=
5x/sqrt5

or, just √5 x, since 5/√5 = √5

Let's go through the steps to verify the simplification of the expression:

(5)^(-1/2) * (5x)^(5/2) * (5x)^(-3/2)

Step 1: Simplify the exponent of the first term using the power rule for exponents: a^(-n) = 1 / a^n.
(5)^(-1/2) = 1 / (5)^(1/2) = 1 / sqrt(5)

Step 2: Simplify the exponent of the second term using the power rule for exponents: (ab)^n = a^n * b^n.
(5x)^(5/2) = (5)^(5/2) * (x)^(5/2) = sqrt(5^5) * sqrt(x^5) = sqrt(5^5 * x^5) = sqrt(5^5x^5)

Step 3: Simplify the exponent of the third term using the power rule for exponents: a^(-n) = 1 / a^n.
(5x)^(-3/2) = 1 / (5x)^(3/2) = 1 / (sqrt(5x)^3) = 1 / (sqrt(5^3 * x^3)) = 1 / (sqrt(5^3) * sqrt(x^3)) = 1 / (sqrt(5^3 * x^3)) = 1 / sqrt(5^3x^3)

Now, let's substitute these simplified terms back into the original expression:

1 / sqrt(5) * sqrt(5^5x^5) * 1 / sqrt(5^3x^3)

Taking the products under one square root:

1 * sqrt(5^5x^5) * 1 / (sqrt(5) * sqrt(5^3x^3))

This simplifies to:

sqrt(5^5x^5) / (sqrt(5) * sqrt(5^3x^3))

Taking out the square roots separately:

(sqrt(5^5) * sqrt(x^5)) / (sqrt(5) * (sqrt(5^3) * sqrt(x^3)))

Simplifying:

(sqrt(5^5) * x^2) / (sqrt(5) * (5 * sqrt(x^3)))

Simplifying further:

(sqrt(5^5) * x^2) / (5 * sqrt(5) * sqrt(x^3))

Simplifying the square root term:

(sqrt(5^5) * x^2) / (5 * sqrt(5) * x(sqrt(x)))

We can cancel out the x term:

(sqrt(5^5) * x^2) / (5 * sqrt(5) * sqrt(x))

Finally, simplifying the square root term:

(sqrt(5^5) * x^2) / (5 * sqrt(5) * sqrt(x)) = (x^2 * sqrt(5^5)) / (5 * sqrt(5) * sqrt(x))

So, the correct simplification is:

(x^2 * sqrt(5^5)) / (5 * sqrt(5) * sqrt(x))

And it cannot be simplified further. Therefore, the answer you provided, x / sqrt(5), is not correct.