Quick exponent rule question

Everyone knows that if you are deviding two terms that have the same bases you subtract the exponents.

Like Z^3/Z^1 = Z^2

However well covering a basic prime factoring subject in a math book the book gives the exaple of an expression being prime factored with the variable Z in the numerator and Z^3 in the denominator and calls it Z^2

How is that possible? Why is it not Z^-2
The z ontop is obviously carries the expontent 1 and last i check 1 - 3 = -2

Someone please explain

Question

Quick exponent rule question

Everyone knows that if you are deviding two terms that have the same bases you subtract the exponents.

Like Z^3/Z^1 = Z^2

However well covering a basic prime factoring subject in a math book the book gives the exaple of an expression being prime factored with the variable Z in the numerator and Z^3 in the denominator and calls it Z^2

How is that possible? Why is it not Z^-2
The z ontop is obviously carries the expontent 1 and last i check 1 - 3 = -2

Someone please explain

anonymous · Answer

Z / Z^3 = 1 / Z^2  or Z^-2

anonymous · Answer

care to elaborate

anonymous · Answer

how does z/Z^3 = 1?

anonymous · Answer

it doesnt. he said  it = 1/z^2 or the negative recip of z^-2

anonymous · Answer

ok so intead of righting the z^-2 the choose to right it as a positive exponent as 1/z^2

anonymous · Answer

makes sense i guess, i wish the book would explain that instead of assuming you know what  its doing