How do you simplify #r^-2/(4r^5*4r^-5)# and write it using only positive exponents?

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Answer 1 · 2017-05-08T09:16:06

#1/(16r^2)#

Note that #1/r^-5# is the same as #5^5# and #r^(-2)# is the same as #1/r^2#

Splitting #r^(-2)/(4r^5xx4r^(-5))# gives:

#1/4xx1/4xx r^(-2)xx1/r^5xx1/r^(-5)#

#1/4xx1/4xx 1/r^2xx1/r^5xxr^(5)#

#1/16xx1/r^2xxr^5/r^5#

But #r^5/r^5=1 larr# This is the same thing as cancelling,

#1/16xx1/r^2=1/(16r^2)#