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

Dec 26, 2016

$= \frac{1}{6}$

#### 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:

$\rightarrow \text{ } {x}^{m} / {x}^{n} = {x}^{m - n}$

Change a negative to a positive index by using the reciprocal

$\rightarrow \text{ "x^-m = 1/x^m" and } \frac{1}{x} ^ - n = {x}^{n}$

$= \frac{\textcolor{b l u e}{{6}^{-} 6}}{6} ^ - 5 = \frac{1}{\textcolor{b l u e}{{6}^{6}} \times {6}^{-} 5}$

$= \frac{1}{6}$

OR:

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

$= {6}^{- 6 + 5}$

$= {6}^{-} 1$

$\frac{1}{6}$

OR:

$\frac{{6}^{-} 6}{6} ^ - 5$

$= \frac{{6}^{5}}{6} ^ 6$

$= \frac{1}{6}$