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#