How do you simplify \frac { \frac { 20t ^ { 3} u } { 7r s ^ { 3} } } { \frac { 5t ^ { 5} u ^ { 4} } { 14s ^ { 4} } }20t3u7rs35t5u414s4?

1 Answer
Jan 31, 2018

(280s)/(35rt^2u^3)280s35rt2u3

Explanation:

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)abcd=(ab)(dc)

So

((20t^3u)/(7rs^3))/((5t^5u^4)/(14s^4))=(20t^3u)/(7rs^3)*(14s^4)/(5t^5u^4)20t3u7rs35t5u414s4=20t3u7rs314s45t5u4

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)(2014)s4t3u(75)rs3t5u4

Now looking at exponents we know that s^4 = s^3 *ss4=s3s

((20*14)color(red)(s^3 * s)t^3u)/((7*5)rcolor(red)(s^3)t^5u^4)(2014)s3st3u(75)rs3t5u4

The s^3s3 cancels out and we use this same process for tt and uu.

Final answer would be

(280s)/(35rt^2u^3)280s35rt2u3