Question

why is a fraction raised to a negative power the same as the multiplicative inverse of that fraction raised to the positive power? why is a fraction raised to a negative power the same as the multiplicative inverse of that fraction raised to the positive power? @Mathematics

Answer 1

Guess its just a property like commutative, associative etc......

Answer 2

pratu is correct, but more specifically it has to do with what an inverse is.

\[a^-1=\frac{1}{a}\]
by definition.

Answer 3

\[a^n*a^m=a^{n+m}\]therefore:\[a^1*a^{-1}=a^{1-1}=a^0=1\]therefore:\[a^{-1}=1/a^1\]

Answer 4

you can use same technique to show:\[a^{-n}=1/a^n\]

Answer 5

@ asnaseer, what textbook do you use brother?

Answer 6

for your specific question, you would get:\[(\frac{a}{b})^{-n}=1/(\frac{a}{b})^n=(\frac{b}{a})^n\]

Answer 7

i don't use any text books as such, I have lernt most of my maths by listening to online lectures (e.g. http://www.khanacademy.org/)