How do you use the quotient property to explain why $x^-n=1/x^n$ ?

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Answer 1 · 2017-05-13T15:03:47

$x^(-n) = x^(0 - n)$

The quotient rule states that $a^(n - m) = a^n/a^m$

$x^0/x^n = 1/x^n$

Hopefully this helps!

Answer 2 · 2017-05-13T15:37:42

$x^-n=1/x^n$

Exponential laws:

$:.a^-n xx a^n=a^(-n+n)$

$:.=a^0=1$

$:.1=a^-n xx n^n$

$:.a^-n=1/a^n$

substitute $color(blue)(1=a^-n xx n^n$

$:.a^-n=color(blue)(a^-n xx n^n)/a^n$

$:.a^-n=a^(-n+n)/a^n$

$:.a^-n=a^0/a^n$

$:.color(blue)(a^-n=1/a^n$

How do you use the quotient property to explain why x^-n=1/x^nx^-n=1/x^n?