How do you simplify #\frac { x ^ { 2/ 3} } { x ^ { 1/ 4} }#?

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Answer 1 · 2017-03-26T05:32:42

#x^(2/3)/x^(1/4)=x^(2/3-1/4)=x^(5/12)#

Let's first rewrite this so we get rid of the divide sign, by using the rule #x^-1=1/x#:

#x^(2/3)x^(-1/4)#

We can now use the rule #x^a xx x^b = x^(a+b)#:

#x^(2/3-1/4)#

I'm going to move the fraction operation out of the #x# term for a second so it can be seen better. Let's combine the fractions:

#2/3-1/4=2/3(4/4)-1/4(3/3)=8/12=3/12=5/12#

Which gives us overall:

#x^(5/12)#

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We could also have gone straight from the fraction:

#x^(2/3)/x^(1/4)=x^(2/3-1/4)=x^(5/12)#