How do you evaluate #\frac{5r\times 5r^{-1}}{-4r^{2}}#?

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Answer 1 · 2017-10-23T16:23:10

See a solution process below:

First, rewrite the expression as:

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

#-25/4((r xx r^-1)/r^2)#

Next, use these rules for exponents to evaluate the numerator of the fraction on the right:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))# and #a^color(red)(0) = 1#

#-25/4((r^color(red)(1) xx r^color(blue)(-1))/r^2) =>#

#-25/4(r^(color(red)(1)+color(blue)(-1))/r^2) =>#

#-25/4(r^0/r^2) =>#

#-25/4(1/r^2) =>#

#-25/(4r^2)#