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

1 Answer
Aug 7, 2017

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

Explanation:

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)