How do you simplify #\frac { \frac { 6q ^ { 5} } { 5r ^ { 4} s ^ { 4} } } { \frac { 3p q ^ { 2} } { 20r ^ { 2} s } }#?

Question

1002 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-07T03:20:19

#((6q^5)/(5r^4s^4))/((3pq^2)/(20r^2s))=(8q^3)/(pr^2s^3)#

Here are some helpful rules to remember:

#(a/b)/(c/d)=a/b*d/c# (1)

#x^a/x^b=x^(a-b)# (2)

#x^-a=1/x^a# (3)

First, apply rule (1)

#((6q^5)/(5r^4s^4))/((3pq^2)/(20r^2s))=(6q^5)/(5r^4s^4)*(20r^2s)/(3pq^2)=(120q^5r^2s)/(15pq^2r^4s^4)#

Now, split up all the factors for clarity

#(120q^5r^2s)/(15pq^2r^4s^4)=120/15*1/p*q^5/q^2*r^2/r^4*s/s^4#

Now, apply rule (2)

#120/15*1/p*q^5/q^2*r^2/r^4*s/s^4=8*1/p*q^(5-2)*r^(2-4)*s^(1-4)=8*1/p*q^3*r^-2*s^-3#

Finally, apply rule (3) and combine all of the factors into a single fraction

#8*1/p*q^3*r^-2*s^-3=8*1/p*q^3/1*1/r^2*1/s^3=(8q^3)/(pr^2s^3)#