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

Question

Give an example to support your answer 

Answer 1

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 

Answer 2

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

Answer 3

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.