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Precalculus

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416
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Factor and express the answer as a quotient with positive exponents.

x^(-2)-4x^(-5)+3x^(-8)

Thank you!!

Aug 30, 2017

#1
+100813
+2

Factor and express the answer as a quotient with positive exponents.

x^(-2)-4x^(-5)+3x^(-8)

$$x^{-2}-4x^{-5}+3x^{-8}\\ =x^{-8}(x^6-4x^3+3)\\ =\frac{x^6-4x^3+3}{x^8}$$

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Aug 30, 2017
#2
+22182
+1

Factor and express the answer as a quotient with positive exponents.

x^(-2)-4x^(-5)+3x^(-8)

$$\begin{array}{|rcll|} \hline && x^{-2}-4x^{-5}+3x^{-8} \\ &=& x^{-8}\left( \frac{x^{-2}} {x^{-8}} - \frac{4x^{-5}} {x^{-8}} +3 \frac{ x^{-8} } {x^{-8}} \right) \\ &=& x^{-8} ( x^{-2} x^{8} - 4x^{-5} x^{8} +3 ) \\ &=& x^{-8} ( x^{-2+8} - 4x^{-5+8} +3 \\ &=& x^{-8} ( x^{6} - 4x^{3} +3 ) \\ &=& x^{-8} (x^3-1)(x^3-3) \\ &=& \dfrac{(x^3-1)(x^3-3)}{x^{8}} \\ \hline \end{array}$$

Aug 30, 2017
#3
+100529
+1

[ ( x^3 - 1) ( x^3 - 3 ) ]           [ ( x - 1) (x^2 + x + 1 ) ( x^3 - 3) ]

_________________   =      __________________________

x^8                                                  x^8

Aug 30, 2017