How do you simplify #\frac { 12x ^ { 2} } { 54x ^ { 3} }#?

1 Answer
EZ as pi
May 25, 2018

#2/(9x)#

Explanation:

#(12x^2)/(54x^3)#

  • Cancel the numbers using common factors. (In this case #6#)
  • subtract the indices of #x#

#=(cancel12^2x^2)/(cancel54_9 x^3)#

#=2/(9x)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Back to basics:
#x^2/x^3 = (cancelx xx cancelx)/(cancelx xx cancelx xx x) =1/x#

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

To avoid ending up with negative indices, 1subtract:
bigger - smaller. The answer will be where the bigger index is.
In this case in the denominator.

Compare:

#x^7/x^3 = x^4" " and " "x^3/x^7 = 1/x^4#

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