Simplify fully (x^2*x^3)/x^4

This question requires knowledge of the rules of indices. 

The first rule we need to use is that when multiplying indices with the same base (which in this case is x), the indices are added. Therefore the expression becomes;

(x²*x³)/x⁴= x⁵/x⁴

The next rule we need to use is that when dividing indices with the same base, we subtract the bottom from the top.  Therefore the expression becomes;

 (x²*x³)/x⁴= x⁵/x⁴ = x¹

Since x¹=x (by the definition of indices x^a means x multiplied by itself a times), the simplest form of (x²*x³)/x⁴ is x.

Answer: x