How do you simplify #\frac { 20r ^ { 8} + 16r^ { 5} } { 4r ^ { 2} } #?

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Answer 1 · 2017-07-27T03:34:58

See a solution process below:

First, rewrite the expression as:

#(20r^8)/(4r^2) + (16r^5)/(4r^2) => (5r^8)/r^2 + (4r^5)/r^2#

We can now use this rule for exponents to simplify each of the fractions:

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

#(5r^color(red)(8))/r^color(blue)(2) + (4r^color(red)(5))/r^color(blue)(2) =>#

#5r^(color(red)(8)-color(blue)(2)) + 4r^(color(red)(5)-color(blue)(2)) =>#

#5r^6 + 4r^3#