Question 541919
a to the -1 half divided by 6a to 1 third times a to the -1 fourth look 
<pre>
I can't tell if you mean this

{{{matrix(3,1,"",(a^(1/2))/(6a^(1/3)),"")  }}}·{{{matrix(3,1,"",a^(1/4),"")}}}or this:  {{{matrix(3,1,"",a^(1/2)/(6a^(1/3)*a^(1/4)),"")  }}}

If it's this one:

{{{matrix(3,1,"",(a^(1/2))/(6a^(1/3)),"")  }}}·{{{matrix(3,1,"",a^(1/4),"")}}}

write the expression {{{matrix(3,1,"",a^(1/4),"")}}} as {{{matrix(3,1,"",(a^(1/4))/1,"")}}}, then you have:

{{{matrix(3,1,"",(a^(1/2))/(6a^(1/3)),"")  }}}·{{{matrix(3,1,"",(a^(1/4))/1,"")}}}


Indicate the multiplication of the numerators and multiplication of
denominators

{{{matrix(3,1,"",(a^(1/2)*a^(1/4))/(6a^(1/3)*1),"") }}}

Add the exponents in the top {{{1/2}}}+{{{1/4}}} = {{{2/4}}}+{{{1/4}}} = {{{3/4}}}

{{{matrix(3,1,"",(a^(3/4))/(6a^(1/3)),"") }}}


Subtract the exponents {{{3/4}}}-{{{1/3}}} = {{{9/12}}}-{{{5/12}}} = {{{5/12}}}

{{{matrix(3,1,"",a^(5/12)/6,"")}}}which can also be written in root form:

{{{1/6}}}{{{root(12,a^5)}}} 

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However, if it's this:

{{{matrix(3,1,"",a^(1/2)/(6a^(1/3)*a^(1/4)),"")  }}}

Add the exponents on the bottom:  {{{1/3+1/4=4/12+3/12=7/12}}}

{{{matrix(3,1,"",a^(1/2)/(6a^(7/12)),"")  }}}

Subtract the exponents {{{1/2 - 7/12=6/12-7/12}}} = {{{-1/12}}}

{{{matrix(3,1,"",a^(-1/12)/6,"")  }}}


Move the negative exponential from the top to the bottom:

{{{matrix(3,1,"",1/(6a^(1/12)),"")  }}}

Write the denominator in root form

{{{1/(6*root(12,a))}}}

Edwin</pre>