Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.


I attempted it many times and got multiple answers which were all wrong... I'll post the one that I think is closest:


\begin{align*} \sqrt[4]{\frac{162x^3y^5}{2x^7y}} & = \sqrt[4]{\frac{81 \cdot 2 \cdot x^3 \cdot y^4 \cdot y}{2 \cdot x^4 \cdot x^3 \cdot y}}\\ & = 3xy \sqrt[4]{\frac{\require{cancel}\cancel{2} \cdot \cancel{x^3} \cdot \cancel{y}}{\cancel{2} \cdot \cancel{x^3} \cancel{y}}}\\ & = 3xy \end{align*}

Please help, the homework is due in under 48 hours and we get 5 tries to submit each answer. I already got this wrong 4 times so I have one final try before the question locks and marks it as wrong.

  • 1
    $\begingroup$ Please see this tutorial on how to typeset mathematics on this site. You can see how I typeset your work by right clicking on a formula, then selecting Show Math As TeX Commands. $\endgroup$ – N. F. Taussig Jun 25 '15 at 8:35

Hint: we can simplify to $$\sqrt[4]{\frac{81y^4}{x^4}}=\frac{3|y|}{|x|}$$

  • $\begingroup$ Oh, so the x goes on the bottom... I considered that but I wasn't sure. Thank you. $\endgroup$ – TheNewGuy Jun 24 '15 at 23:31

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