Question

How do you simplify `6^-6/6^-5`?

Answer 1

`= 1/6`

Explanation:

There are 2 laws of indices going on here - you can apply them in any order. Use whichever method you prefer.
Answers are usually given with positive indices.

(An exception in with scientific notation where a negative index means the number is a decimal fraction.)

When dividing, subtract the indices of like bases:

`rarr" "x^m/x^n = x^(m-n)`

Change a negative to a positive index by using the reciprocal

`rarr" "x^-m = 1/x^m" and "1/x^-n = x^n`

`=color(blue)(6^-6)/6^-5 = 1/(color(blue)(6^6) xx6^-5)`

`= 1/6`

OR:

`(6^-6)/6^-5 = 6^(-6-(-5)`

`=6^(-6+5)`

`=6^-1`

`1/6`

OR:

`(6^-6)/6^-5`

`=(6^5)/6^6`

`=1/6`