How do you multiply and simplify \frac { 3p ^ { 4} } { 5q ^ { 5} ( r - 5) ^ { 3} } \cdot \frac { 4l q ^ { 2} ( r - 5) } { 21p ^ { 3} }?

1 Answer
Apr 17, 2017

(4pl)/(35q^3(r-5)^2)

Explanation:

(color(green)3p^color(red)4)/(5q^5(r-5)^3)*(4lq^2(r-5))/(color(green)21p^color(red)3)

Subtract the smaller exponent of a base from both bases, because of the division, and simplify 3 and 21 by dividing them by 3

(cancel3p^(4-3))/(5q^5(r-5)^3)*(4lq^2(r-5))/(7cancel21cancel(p^(3-3)))

Anything to the power of zero can be cancelled

(r-5) is the same as (r-5)^1

=p/(5q^5(r-5)^color(red)3)*(4lq^2(r-5)^color(red)1)/7

=p/(5q^5(r-5)^(color(red)3-1))*(4lq^2cancel((r-5)^(color(red)1-1)))/7

=p/(5q^color(red)5(r-5)^2)*(4lq^color(red)2)/7

=p/(5q^(color(red)5-2)(r-5)^2)*(4lcancel(q^(color(red)2-2)))/7

=p/(5q^3(r-5)^2)*(4l)/7

Now there is no other simplification, we will multiply these two expressions together

=(p*4l)/(color(green)5q^3(r-5)^2*color(green)7)

=(4pl)/(35q^3(r-5)^2)

After a final check, this is the most simplified form.