The requested form $x^ay^b$ with fixed integer indices requires a sign condition: for \(y

Question

The requested form $x^ay^b$ with fixed integer indices requires a sign condition: for $y>0$, the answer is $x^6y^{-5}$. For arbitrary nonzero real $x,y$, the principal-root answer is $x^6/|y|^5$. Express ${{\left( \frac{{{x}^{3}}{{y}^{-4}}}{{{x}^{-9}}{{y}^{6}}} \right)}^{\frac{1}{2}}}$ in the form ${{x}^{a}}{{y}^{b}}$, where $a$ and $b$ are integers.

Accepted Answer

$x^6/|y|^5$; for $y>0$, $x^6y^{-5}$ and $a=6,b=-5$.

Expressing Powers in Simplified Index Form

Expressing Powers in Simplified Index Form

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