If you write the following expression

Question

(x^-3 x^2 / x^3 x^-2) 

as a single power of x then the exponent is

Answer 1

It looks like you mean:

 

x^-3 x² 

--------

x³ x^-2

 

 

When you multiply powers of the same value (x), you ADD the exponents.  So this becomes:

 

x^{-3 + 2} / x^{3 + -2} = x^-1 / x¹

 

When you divide powers of the same value, you SUBTRACT the exponents:

 

x^-1 / x¹ = x^{-1 -1} = x^-2

 

So the single exponent is -2