Question 30258

x5^-2/x^3
If the problem is (x) multiplied by [5^(-2)] divided by (x^3)
then it is 
(x)X [5^(-2)]/(x^3)
= [1/5^2]X[1/(x^3)X(x^-1)]   
(using rule (a)^(-m) = 1/[(a)^m] and here a = 5 and m= 2 )----(*)
(And (a)^(m) = 1/[(a)^(-m)] where here a = x and m= 1)
=(1/25)X[1/x^(3-1)] 
(when quantities of the same base are multiplied write the base and add the powers.)
=1/(25x^2)


And if the problem is [(x^5)^(-2)]/x^3
= {x^[5X(-2)]}/x^3  (using [(a)^m]^n =a(mn) where here a = x, m= 5 and n = -2 )
= x^(-10)/x^3
= (1/x^10)X(1/x^3)  (using (*) )
=1/[x^(10+3)](when quantities of the same base are multiplied write the base and add the powers.)
= 1/(x^13)