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

Mar 18, 2016

$= 6 {x}^{- \frac{1}{3}}$

#### 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

$6 {x}^{- \frac{1}{3}}$

#### Explanation:

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

$\frac{6 \times 2}{2} \times \frac{{x}^{- \frac{4}{3}} \times {x}^{\frac{2}{3}}}{{x}^{- \frac{1}{3}}}$

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$\text{ "(x^(-4/3)xxx^(2/3))/(x^(-1/3))" is the same as } \frac{{x}^{\frac{1}{3}} \times {x}^{\frac{2}{3}}}{{x}^{\frac{4}{3}}}$

$\textcolor{b r o w n}{\text{'~~~~~~~~~~~~~~~~~ Note ~~~~~~~~~~~~~~~~~~~~~~~}}$
$\textcolor{b r o w n}{\text{If you have for example "a^2xxa^3" then this is the same as}}$
$\textcolor{b r o w n}{{a}^{2 + 3} \text{. The same happens with fractional powers.}}$
$\textcolor{b r o w n}{\text{'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}}$

$\text{ "(x^(1/3)xx x^(2/3))/(x^(4/3))" " =" } \frac{{x}^{\frac{1}{3} + \frac{2}{3}}}{{x}^{\frac{4}{3}}}$

$\text{ } = \frac{{x}^{\frac{3}{3}}}{{x}^{\frac{4}{3}}}$

$\textcolor{b r o w n}{\text{'~~~~~~~~~~~~~~~~~ Note ~~~~~~~~~~~~~~~~~~~~~~~}}$
$\textcolor{b r o w n}{\text{If you have for example "a^2/a^3" then this is the same as}}$
$\textcolor{b r o w n}{{a}^{2 - 3} \text{. The same happens with fractional powers.}}$
$\textcolor{b r o w n}{\text{'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}}$

$\text{ } = \frac{{x}^{\frac{3}{3}}}{{x}^{\frac{4}{3}}}$

$\text{ } = {x}^{\frac{3 - 4}{3}}$

$\text{ } = {x}^{- \frac{1}{3}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Combining with the numbers}}$

$\text{ } \textcolor{red}{= 6 {x}^{- \frac{1}{3}}}$