Help with simplification

  • #1

Homework Statement


Om a > 0, b > 0, c > 0, och x = ((ab√c)1/3-a(b2c)1/4)/(a3b2c)1/6

The Attempt at a Solution



I have no idea where to start. I understand the relevance of a,b and c being > 0 in order to simplify but other than that I am pretty much stuck!
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
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A first obvious step is to replace that [itex]\sqrt{c}[/itex] with [itex]c^{1/2}[/itex]. Then use the "laws of exponentials: [itex](abc^{1/2})^{1/3}= a^{1/3}b^{1/3}c^{1/6}[/itex], [itex]a(b^2c)^{1/4}= ab^{1/2}c^{1/4}[/itex] and [itex](a^3b^2c)^{1/6}= a^{1/2}b^{1/3}c^{1/6}[/itex]

So you have [tex]\frac{a^{1/3}b^{1/3}c^{1/6}- ab^{1/2}c^{1/4}}{a^{1/2}b^{1/3}c^{1/6}}[/tex]

Factor the largest power of a, b, and c in both terms in the numerator and cancel what you can with the denominator.
 
  • #3
\begin{align*}
\frac{\sqrt[3]{ab \sqrt{c}} - a \sqrt[4]{b^2 c}}{\sqrt[6]{a^3 b^2 c}}
\end{align*}

Wrote the equation in latex too, it was easier to see.
 
  • #4
Alright that was easier than I previously thought! Thanks!
 

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