How do you simplify $x^{- 4} (x^{2} + x - 3)$ $x^-4 (x^2 + x - 3)$ ?

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How do you simplify $x^{- 4} (x^{2} + x - 3)$ $x^-4 (x^2 + x - 3)$ ?

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Answer 1 · 2015-06-15T12:10:12

$= x^{- 2} + x^{- 3} - 3 . x^{- 4}$ $= color(blue)(x^-2 + x^-3 - 3.x^-4$

Explanation:

$x^{- 4} (x^{2} + x - 3)$ $x^-4 (x^2 + x - 3)$

Here , we need to multiply $x^{- 4}$ $color(red)(x^-4$ with every term within the bracket.

$x^{- 4} . x^{2} + x^{- 4} . x^{1} - x^{- 4} .3$ $color(red)(x^-4) .x^2 +color(red)( x^-4).x^1 -color(red)( x^-4).3$

Note:
$a^{m} . a^{n} = a^{m + n}$ $color(blue)(a^m . a^n = a^(m+n)$
Applying the above mentioned property to the exponents of $x$ $x$

$= x^{- 4 + 2} + x^{- 4 + 1} - (x^{- 4}) .3$ $= x^(-4+2) + x^(-4+1) - (x^-4).3$
$= x^{- 2} + x^{- 3} - (x^{- 4}) .3$ $= x^-2 + x^-3 - (x^-4).3$
$= x^{- 2} + x^{- 3} - 3 . (x^{- 4})$ $= color(blue)(x^-2 + x^-3 - 3.(x^-4)$

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How do you simplify $x^{- 4} (x^{2} + x - 3)$ $x^-4 (x^2 + x - 3)$ ?

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