How do you divide #10r ^ { - 3} \div - 2r ^ { 2}#?

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Answer 1 · 2016-12-22T14:01:42

#5/r^5# or #5r^-5#

The expression #10r^-3 -: -2r^2# can be rewritten as:

#(10r^-3)/(2r^2)#

One of the rules for exponents states:

#color(red)(x^a/x^b = 1/x^(b - a))#

Using this rule the expression will change to:

#10/(2r^(2 - (-3))#

#10/(2r^5)#

And #10/2 = 5# so we can modify the expression again to:

#5/r^5#

Another solution would use the rue for exponents stating:

#color(red)(x^a/x^b = x^(a-b))#

This would give:

#(10r^(-3 - 2))/2#

#(10r^(-5))/2#

#5r^-5#