(x^3y^-2)^2/(x^5y^3)^-3

Question

simplify and write the resulting expression with only positive exponents

Answer 1

(x³y^-2)²/(x⁵y³)^-3

 

Remembering that x^-a = 1/x^a, we can re-write the expression as:

 

(x³)²(x⁵y³)³/(y²)²

 

Now (x^a)^b = x^ab:

 

x⁶x¹⁵y⁹/y⁴

 

Since x^ax^b = x^a+b  and x^a/x^b = x^a-b, we can combine terms with the same base and simplify:

 

x⁶⁺¹⁵y^9-4

 

x²¹y⁵