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

1/sqrt5 x sqrt5x^5 x 1/sqrt5x^3=
??? I need to simplify and I need help understanding what the next step is

after more simplification I got

x^2(sqrt5x)/(sqrt5)(x sqrt5x)
can I cancel out the sqrt5x from the denominator and numerator?

Is the final answer x/sqrt5?

need in layman's terms, please, thank you

I have a hard time parsing the factors, since you eschew parentheses. Why don't you enter your expression at wolframalpha.com and confirm your work. I tried to get it right at

http://www.wolframalpha.com/input/?i=5^%28-1%2F2%29+x+%285x%29^%285%2F2%29+%285x%29^%28-3%2F2%29

See what you think, and fix it if I garbled the syntax. You seem to have a handle on things, and wolframalpha is a great resource.

I will say that working from your last line, you clearly have a √5x top and bottom, which can cancel:

x^2(sqrt5x)/(sqrt5)(x sqrt5x)
= x^2 √(5x) / (√5 x√(5x))
= x^2/x√5 * √(5x)/√(5x)
= x/√5

To simplify the given expression, let's break it down step by step.

Step 1: Simplify each term separately
5^-1/2 can be written as 1/sqrt5.
5x^5/2 can be written as sqrt(5x)^5.
(5x)^-3/2 can be written as 1/(sqrt(5x)^3).

Now the expression becomes:
1/sqrt5 x sqrt(5x)^5 x 1/(sqrt(5x)^3)

Step 2: Apply exponent rules
The exponent rule states that when you have a power raised to another power, you multiply the exponents.

In this case, we can rewrite the expression as:
1/sqrt5 x (sqrt(5x))^5 x 1/((sqrt(5x))^3)

Step 3: Simplify the exponents
(sqrt(5x))^5 means taking the square root of 5x and raising it to the power of 5. Similarly, (sqrt(5x))^3 means taking the square root of 5x and raising it to the power of 3.

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

Now the expression becomes:
1/sqrt5 x (5x)^(5/2) x 1/(5x)^(3/2)

Step 4: Apply the multiplication and division rules
When dividing two exponential terms with the same base, subtract the exponents. So, we can rewrite the expression as:
(1/sqrt5) * (5x)^(5/2 - 3/2)
= (1/sqrt5) * (5x)^1

Step 5: Simplify further
(5x)^1 means raising 5x to the power of 1, which is simply 5x.

So the final simplified expression is:
(1/sqrt5) * (5x)

Alternatively, you can rewrite it as:
5x/sqrt5, which is an equivalent form of the simplified expression.

Therefore, 5^-1/2 x 5x^5/2(5x)^-3/2 simplifies to 5x/sqrt5 or 1/sqrt5 x sqrt5x^5 x 1/sqrt5x^3 simplifies to 5x/sqrt5.