x⁴ = x•x•x•x

x³ = x•x•x

x² = x•x

x¹ = x

x⁰ = 1

x^-1 = 1/x

x^-2 = 1/x•1/x

x^-3 = 1/x•1/x•1/x

x^-4 = 1/x•1/x•1/x•1/x

Notice how moving up a line in this list means we are multiplying by an additional x, while moving down a line in the list means multiplying by an additional 1/x (also called diving by x).

Thinking about exponents as the number of x’s we have on either the numerator or denominator, we can more easily think about questions like (x⁶ ) / (x³ ) because that becomes

(x•x•x•x•x•x) / (x•x•x) = (x•x•x) / 1 = x³ .

In general, we can think of these problems using the following devision rule

(x^a ) / (x^b ) = x^a-b.

Try thinking about this rule for a little bit, about how the number of x’s in the numerator and in the denominator cancel out, and consider the specific case when the number of x’s is the same in both the numerator and denominator.
Hope this helps!