How do you simplify #\frac { \frac { 20t ^ { 3} u } { 7r s ^ { 3} } } { \frac { 5t ^ { 5} u ^ { 4} } { 14s ^ { 4} } }#?

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Answer 1 · 2018-01-31T22:28:24

#(280s)/(35rt^2u^3)#

Key point here is Dividing by a fraction is the same thing as multiplying by its reciprocal.

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

So

#((20t^3u)/(7rs^3))/((5t^5u^4)/(14s^4))=(20t^3u)/(7rs^3)*(14s^4)/(5t^5u^4)#

From here, since we are multiplying fractions we can simply put everything together. (AKA combine like terms)

#((20*14)s^4t^3u)/((7*5)rs^3t^5u^4)#

Now looking at exponents we know that #s^4 = s^3 *s#

#((20*14)color(red)(s^3 * s)t^3u)/((7*5)rcolor(red)(s^3)t^5u^4)#

The #s^3# cancels out and we use this same process for #t# and #u#.

Final answer would be

#(280s)/(35rt^2u^3)#