Is the following statement always, never, or sometimes true?
A number raised to a negative exponent is negative.
always
never**
sometimes
4^-2 = 1/4^2 = 1/16 <----- positive
(-4)^-2 = 1/(-4)^2 = 1/16 <------ positive
(-4)^-3 = 1/(-4)^3 = 1/-64 <----- negative
mhhhh ?
So the answer is sometimes right?
The correct answer is never.
To understand why, we need to review the rules of exponents. When a number is raised to a negative exponent, it is written as 1 divided by that number raised to the positive exponent. In other words, a^(-n) = 1/a^n.
For example, let's consider the number 2 raised to the power of -2: 2^(-2) = 1/2^2 = 1/4. As we can see, the result is positive, not negative.
Similarly, for any number raised to a negative exponent, the result will always be a positive value. Therefore, the statement "A number raised to a negative exponent is negative" is never true.