SOLUTION: Please help me solve this problem: (5thrt5x^2y)^9 It is the 5th root of 5x squared time y; all to the 9th power

You don't "solve" it.  You only solve equations and inequalities.

You can only simplify or rewrite expressions.  You didn't quote
the instructions for how you are to simplify or rewrite the
expression.  There are two sets of instructions your teacher
or book could have been talking about.

First possible instructions:
Rewrite using no radicals (roots), using
only fractional exponents.  Then we would
rprecede this way:



replace  by 



Remove the outermost parentheses by multiplying
the exponents  and  to get
exponent 



Now we remove the parentheses by writing 
as 



And multiplying each inner exponent,  and 
by the outer exponent , getting




-------------

However if the instructions are to rewrite in simplest radical form,

then you do it this way instead:



Bring the exponent 9 inside the radical:



Give the  an eponent of 



Remove the parentheses by multiplying inner exponents
by the outer exponent.





Since both inside exponents are larger than the index
5, we do this division by the index of the radical, 5:


   3         1
 ---         -
5)18       5)9
  15         5
  --         -
   3         4  

The quotients are the exponents of their bases IN FRONT
OF the radical and the remainders are the powers UNDER
the radical.




Edwin