What is (x-3)^-1 multiplied by (x-3)^-2?

[(x - 3)^-1][(x - 3)^-2]
= (x - 3)^[(-1) + (-2)]
= (x - 3)^[-1 - 2]
= (x - 3)^-3
= 1/(x - 3)^3

(x-3)^-3 (You add the exponents -1 - 2 = -3)

(x-3)^-3
Add exponents.

(x - 3)^(-1) (x - 3)^(-2) = (x - 3)^(-3) = 1 / (x - 3) ³

Add the exponents.

You first remove all negative exponents in both equations. You'll get:

1
------
(x-3)

and

1
----------
(x-3)^2

Multiply the fractions so you will add the exponents to get:

1
---------
(x-3)^3

You ADD the exponents when multiplying the terms.

Confused? Try a simple example:

2^3 * 2^4

This is 8 * 16 = 128, which is 2^7, NOT 2^8.