How do you multiply and simplify #\frac { 12} { 5x } \times \frac { x ^ { 3} } { 12x }#?

1 Answer
Mar 4, 2017

#x/5#

Explanation:

Multiply the top and bottom together, so

#12/(5x)xxx^3/(12x) = (12xxx^3)/(5x xx 12x) = (12x^3)/(60x^2)#

Now we have effectively two fractions, one with numbers and one with #x#'s:

#(12x^3)/(60x^2) = 12/60 xx x^3/x^2#

The #12/60# fraction simplifies to #1/5# because

#12/60 = (12*1)/(12*5) = (cancel(12)*1)/(cancel(12)*5) = 1/5#

and the #x^3/x^2# fraction, by rules of indices, subtracts the powers, so

#x^3/x^2=x^(3-2)=x^1=x#

The whole thing, then, becomes

#x * 1/5 = x/5#