How do you simplify and write $\frac{{(x^{2})}^{- 3} (x^{- 2})}{{(x^{2})}^{- 4}}$ $((x^2)^-3(x^-2) )/ (x^2)^-4$ with positive exponents?

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How do you simplify and write $\frac{{(x^{2})}^{- 3} (x^{- 2})}{{(x^{2})}^{- 4}}$ $((x^2)^-3(x^-2) )/ (x^2)^-4$ with positive exponents?

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Answer 1 · 2016-04-05T10:53:38

$1$ $1$

Explanation:

Given: $\frac{{(x^{2})}^{- 3} (x^{- 2})}{{(x^{2})}^{- 4}}$ $(color(brown)((x^2)^(-3))color(red)((x^-2)))/(color(blue)((x^2)^(-4)))$

${(x^{2})}^{- 3} = x^{- 6} = \frac{1}{x^{6}}$ $color(brown)((x^2)^-3) = x^-6 = 1/x^6$

$(x^{- 2}) = \frac{1}{x^{2}}$ $color(red)((x^-2)) = 1/x^2$

$\frac{1}{{(x^{2})}^{- 4}} = \frac{1}{x^{- 8}} = x^{8}$ $1/(color(blue)((x^2)^-4))=1/x^-8=x^8$

$\frac{{(x^{2})}^{- 3} (x^{- 2})}{{(x^{2})}^{- 4}} = {(x^{2})}^{- 3} \times (x^{- 2}) \times \frac{1}{{(x^{2})}^{- 4}}$ $(color(brown)((x^2)^(-3))color(red)((x^-2)))/(color(blue)((x^2)^(-4)))=color(brown)((x^2)^-3)xxcolor(red)((x^-2))xx1/(color(blue)((x^2)^-4))$

$XXXXXXXX = \frac{1}{x^{6}} \times \frac{1}{x^{2}} \times \frac{x^{8}}{1}$ $color(white)("XXXXXXXX")=1/x^6xx1/x^2xxx^8/1$

$XXXXXXXX = \frac{x^{8}}{x^{8}}$ $color(white)("XXXXXXXX")=x^8/x^8$

$XXXXXXXX = 1$ $color(white)("XXXXXXXX")=1$

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How do you simplify and write $\frac{{(x^{2})}^{- 3} (x^{- 2})}{{(x^{2})}^{- 4}}$ $((x^2)^-3(x^-2) )/ (x^2)^-4$ with positive exponents?

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