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(x^(3/2))^(1/6)

___________

(x^(2/3))^(1/6)

 

simplify and use only positive exponents

Guest Sep 18, 2017
 #1
avatar+7455 
0

(x^(3/2))^(1/6)

___________

(x^(2/3))^(1/6)

simplify and use only positive exponents

 

\((x^\frac{3}{2})^\frac{1}{6}/(x^\frac{2}{3})^\frac{1}{6} \)

\(=x^\frac{1}{4}/x^\frac{1}{9}\\ =x^{\frac{1}{4}-\frac{1}{9}}\\ \color{blue}=x^{\frac{5}{36}}\) 

 

laugh  !

asinus  Sep 18, 2017
 #2
avatar+20016 
0

(x^(3/2))^(1/6)

___________

(x^(2/3))^(1/6)

 

simplify and use only positive exponents

 

\(\begin{array}{|rcll|} \hline && \dfrac{ (x^{\frac{3}{2}} )^{ \frac{1}{6} } } { (x^{\frac{2}{3}})^{ \frac{1}{6} } } \\ &=& \left(\dfrac{ x^{\frac{3}{2}} } { x^{\frac{2}{3}} } \right)^{ \frac{1}{6} } \\ &=& \left(x^{\frac{3}{2}} \cdot x^{-\frac{2}{3}} \right)^{ \frac{1}{6} } \\ &=& \left(x^{\frac{3}{2}-\frac{2}{3}} \right)^{ \frac{1}{6} } \\ &=& \left(x^{\frac{9-4}{6}} \right)^{ \frac{1}{6} } \\ &=& \left(x^{\frac{5}{6}} \right)^{ \frac{1}{6} } \\ &=& x^{\frac{5}{6}\cdot\frac{1}{6} } \\ &=& x^{\frac{5}{36}} \\ \hline \end{array} \)

 

laugh

heureka  Sep 19, 2017

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