Question

(4/9)-¹ ?????????? what is it? -9/4 -4/9 9/4

Answer 1

Im not sure on the syntax here, but i assume the question is (4/9)^-1

(4/9)^-1
= (4^-1)/(9^-1)

A negative power is an inverse of the positive power
i.e. x^-2 = 1/x^2
This is because if we have say x^3/x^5 we simplify it by cancelling x^3 which gives 1/x^2.
Another way to think of it is to subtract the power of the bottom x from the power of the top x: 3-5 = -2 so x^3/x^5 = x^-2.
I hope this explains how negitive powers are the inverse of the positive power.

So....
(4^-1)/(9^-1)
= 9/4
Because the inverse of 4 is 1/4 and the inverse of 1/9 is 9