How do you simplify #[6x^(-4/3) * 2x^(2/3)] / (2x^(-1/3))#?

2 Answers
Mar 18, 2016

Answer:

#= 6x^(-1/3)#

Explanation:

#(6x^(-4/3)*cancel2x^(2/3))/(cancel2x^(-1/3))=6x^(-4/3+2/3+1/3=6x^(-4/3+1)= 6x^(-1/3)#

Mar 18, 2016

Answer:

#6x^(-1/3)#

Explanation:

As the powers are not applied to the numbers you cane split it like this:

#(6xx2)/2 xx(x^(-4/3)xxx^(2/3))/(x^(-1/3))#

#color(blue)("For the number we have "6xx2/2" " =" " 6xx1" " =" " 6#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The powers being negative means they go to the other side of the 'line' and in doing so changing from negative to positive.

So#" "(x^(-4/3)xxx^(2/3))/(x^(-1/3))" is the same as "(x^(1/3)xx x^(2/3))/(x^(4/3))#

#color(brown)("'~~~~~~~~~~~~~~~~~ Note ~~~~~~~~~~~~~~~~~~~~~~~")#
#color(brown)("If you have for example "a^2xxa^3" then this is the same as")#
#color(brown)(a^(2+3)". The same happens with fractional powers.")#
#color(brown)("'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")#

#" "(x^(1/3)xx x^(2/3))/(x^(4/3))" " =" " (x^(1/3+2/3))/(x^(4/3))#

#" "= (x^(3/3))/(x^(4/3))#

#color(brown)("'~~~~~~~~~~~~~~~~~ Note ~~~~~~~~~~~~~~~~~~~~~~~")#
#color(brown)("If you have for example "a^2/a^3" then this is the same as")#
#color(brown)(a^(2-3)". The same happens with fractional powers.")#
#color(brown)("'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")#

#" "= (x^(3/3))/(x^(4/3)) #

#" "= x^((3-4)/3)#

#" " = x^(-1/3)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Combining with the numbers")#

#" "color(red)(=6x^(-1/3))#