How do you multiply and simplify #-\frac { 5m ^ { 5} } { 63n } \cdot \frac { 81m n } { 40m ^ { 7} }#?

1 Answer
Apr 27, 2018

Answer:

See a solution process below:

Explanation:

First, rewrite the expression as:

#(-5 * 81)/(63 * 40)((m^5 * m)/m^7)(n/n) =>#

#(-5 * 81)/(63 * 40)((m^5 * m)/m^7)1 =>#

#(-5 * 81)/(63 * 40)((m^5 * m)/m^7) =>#

#(-5 * 9 * 9)/(9 * 7 * 8 * 5)((m^5 * m)/m^7) =>#

#(-color(red)(cancel(color(black)(5))) * color(blue)(cancel(color(black)(9))) * 9)/(color(blue)(cancel(color(black)(9))) * 7 * 8 * color(red)(cancel(color(black)(5))))((m^5 * m)/m^7) =>#

#-9/56((m^5 * m)/m^7)#

Next, use these rules for exponents to simplify the #m# terms in the numerator:

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

#-9/56((m^5 * m)/m^7) =>#

#-9/56((m^color(red)(5) * m^color(blue)(1))/m^7) =>#

#-9/56(m^(color(red)(5)+color(blue)(1))/m^7) =>#

#-9/56(m^6/m^7)#

Now, use these rules of exponents to complete the simplification:

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

#-9/56(m^color(red)(6)/m^color(blue)(7)) =>#

#-9/56(1/m^(color(blue)(7)-color(red)(6))) =>#

#-9/56(1/m^1) =>#

#-9/56(1/m) =>#

#-9/(56m)#