True of false a number raised to a negative power is always a negative number?

false. it will only be negative if the number is negative with an odd exponent. what you're actually doing is dividing instead of multiplying. for example:

4² = 16

4^-2 = 1/16

basically, it is

x^-n =1/xⁿ 

It is false.

Take a look at why negative exponents will never be negative if the number inside is positive.

Suppose we have x²/x³

By law of exponents, we subtract the exponents since the bases are the same.

So x^2-3= x^-1

And x*x / x*x*x = 1/x

Therefore, x^-1 = 1/x

Only time a number to a negative exponent is negative, is when
1) Number inside is negative
2) exponent is an odd number

Statement is false. Result can be negative or positive it depends from the base and exponent.

If base is negative number, there are two possibilities: 
  - result is negative, if exponent is odd number; (-2)^-3 = 1/(-2)³ = - (1/8)
  - result is positive, if exponent is even number; (-2)^-2 = 1/(-2)² = 1/4

If base is positive number, the result is always positive:
       2^-3 = 1/2³ = 1/8
       2^-2 = 1/2² = 1/4

Very important to remember, if exponent is negative number, that base can't be zero.