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

1 Answer
Dec 26, 2016

Answer:

#= 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#