Question

what power to 1/3 = -9

Answer 1

the power is 1/3?

Answer 2

yes

Answer 3

Except... it would have to be to the - 1/3 in order to generate a negative number?

Answer 4

here is the problem (1/3)^x=-9

Answer 5

The power of (1/3) (ie. x^(1/3)) is the same as taking the cubed root of the number. Taking a negative power results in a fraction (ie. x^-1 = 1/x). So...

\[\sqrt[3]{x}=-9\]
\[x=(-9)^3=-729\]

Answer 6

Misinterpreted the problem. Upon further looking, it seems this problem is not easy at all as it includes logs and imaginary numbers. The answer can be found at http://www.wolframalpha.com/input/?i=%281%2F3%29^x%3D-9

Answer 7

thank you so much!

Answer 8

1/3 = -9
3*(-1)= (3i)*2
- so from 1/3 on indifferent power you not can making -9 never

Answer 9

there is no way of raising
\[\frac{1}{3}\] to a power and getting a negative number.