Question 29173
x^1/3 multiplied by x^5/2, divided by x^-1/5 

-- the directions on the problem say "simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive when they appear."

x^1/3 multiplied by x^5/2, divided by x^-1/5 

(x^1/3  X x^5/2)/( x^-1/5)
=x^(1/3+5/2)X [1/x^(-1/5)]   {  [something]/t = {that something X(1/t) }(example: (a/b) = aX(1/b)  )
=x^(1/3+5/2)X x^(1/5)   (using  1/[a^(-m)] =(a)^(m)
=x^[(2X1+3X5)/6] X  [x^(1/5)] [using (a)^m X(a)^n = (a)^(m+n)] (and finding the lcm)
=x^(17/6) X  x^(1/5)
=x^(17/6+1/5)  [using (a)^m X(a)^n = (a)^(m+n)]
=x^[(5X17+6X1)/30]  (finding the lcm)
=x[(85+6)/30]
=x^(91/30)