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How do you simplify $\frac{\sqrt[5]{12}}{4 \sqrt[5]{- 4}}$ $root5(12)/(4root5(-4))$ ?

2 Answers

Apr 15, 2017

$\frac{\sqrt[5]{12}}{4 \sqrt[5]{- 4}} = - \frac{\sqrt[5]{3}}{4}$ $(root5(12))/(4root5(-4))=color(red)(-root5(3)/4)$

Explanation:

$\frac{\sqrt[5]{12}}{4 \sqrt[5]{- 4}}$ $root5(12)/(4root5(-4)$

$color(white)("XXX")=(root5(3) * cancel(root5(4)))/(4 * root5(-1) * cancel(root5(4)))$

$color(white)("XXX")=root5(3)/(4 * (-1))$

$color(white)("XXX")=-root5(3)/4$

Apr 15, 2017

$color(red)(=-root5(3)/4$ or $color(red)(=-0.311432734$

Explanation:

$root5(12)/(4root5(-4)$

$:.=(root5(3) * cancelroot5(4)^color(red)1)/(4 * cancelroot5(4)^color(red)1* root5(-1) )$

$:.=root5(3)/(4 * (-1))$

$:.color(red)(=-root5(3)/4$

$:.color(red)(=-0.311432734$

Alternative method:

$:.=12^(1/5)/(4*(-4)^(1/5))$

$:.=12^0.2/(4*(-4)^0.2)$

using the calculator:

$:.=1.64375183/(4*-1.319507911)$

$:.=1.64375183/(-5.278031644)$

$:.color(red)(=-0.311432734$

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