how do you simplify this expression?

Question

...using only positive exponents?

135/2 * (4-9x)^(-1/2)
(that's 135 halves times 4-9x to the negative one half power, incase that's a little weird to read :P)

Answer 1

When you see a negative exponent (in this case, "-1/2"), it means that the term is on the wrong side of the division line to be in the simplified form. When you move the term to the other side of the division line, you change the negative exponent to a positive one. Therefore, your original equation:
135/2 * (4-9X)^(-1/2)
becomes
135/[2(4-9X)^(1/2)]
In words, that is 135 divided by (two times (4-9X) to the one half power).
Remember that taking something to the 1/2 power is to find the square root of that something. Here, you are looking at the square root of (4 - 9X)

Answer 2

Remember that the order of math operations is PEMDAS. (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.)
135/2=67.5
(4-9x)^ -.5 is equivalent to 1 over (4-9x)^.5
So..... you now have
(67.5)/((4-9x)^.5)
You can't do much else with that because (4-9x) ^.5 is the same thing as the square root of (4-9x).
(4-9x) is not a perfect square so it can really be simplified past this.
Make sure that you have copied/presented the problem correctly because parentheses in the problem could change your answer.