How do you simplify #\frac { - 20a ^ { 3} b ^ { 8} c ^ { 4} } { 28a ^ { 3} b ^ { 7} c ^ { 5} }#?

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Answer 1 · 2016-12-27T13:24:46

#-(5b)/(7c)#

There are four rules of exponents we will need to utilize in order to simplify this expression:

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

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

#color(green)(x^0 = 1)#

#color(purple)(x^1 = x)#

Understanding these rules we can now simplify this expression as follows:

First, we can factor the constants.

#(-20a^3b^8c^4)/(28a^3b^7c^5) -> (-(4 xx 5)a^3b^8c^4)/((4 xx 7)a^3b^7c^5) -> (-( cancel(4) xx 5)a^3b^8c^4)/((cancel(4) xx 7)a^3b^7c^5)#

#(-5a^3b^8c^4)/(7a^3b^7c^5)#

Now, we can deal with the terms with exponents:

#(-5color(red)(a^(3-3)b^(8-7)))/(7color(blue)(c^(5-4))) -> (-5color(green)(a^0)color(purple)(b^1))/(7color(purple)(c^1)) -> (-5 xx 1 xx b)/(7 xx c)#

#(-5b)/(7c)#