assume that all variables represent positive real numbers

Question

( x^3/2y^-4/2z^5/6 / x^3/2y^4/5z^-2/4)⁶

Answer 1

Use the property of exponents that  x^a / x^b = x^(a-b) to determine the powers of the variables inside the parentheses.  

 

Then use the property that  (x^a)^b = x^(a*b).  

 

You can simplify your answer by getting rid of any negative exponents using the property that x^-a = 1 / x^a,  and you can also pull out integer powers from any improper fractions (for example x^4/3 = x*x^1/3).