Write ( x^3/2)^4/3]*(x^1/4)/x as x raised to a power.

We'll write the first term of the product from
numerator as:

(x^m)^n = x^(m*n), where m = 3/2 and n =
4/3

(x^3/2)^4/3 =
x^(3*4/2*3)

We'll simplify and we'll
get:

(x^3/2)^4/3 = x^2

Now,
we'll solve the product from
numerator:

[(x^3/2)^4/3]*(x^1/4) =
(x^2)*(x^1/4)

Since the bases are matching, we'll add the
exponents:

(x^2)*(x^1/4) = x^(2 +
1/4)

x^(2 + 1/4) = x^9/4

Now,
we'll solve the ratio:

 x^9/4/x = x^(9/4 -
1)

x^(9/4 - 1) =
x^5/4