A number raised to a negative exponent is negative.
a. always
b. never
c. sometimes *****
Now let me see.
3^-2 = 1/3^2 = 1/9
(-3)^-2 = 1/(-3)^2 = 1/9
3^-1 = 1/3^1 = 1/3
(-3)^-1 = 1/(-3)^1 = -1/3
well, looks like I agree with you
To determine whether a number raised to a negative exponent is negative, we need to understand the properties of exponents.
The rule for negative exponents states that when a number is raised to a negative exponent, it can be rewritten as the reciprocal of the number raised to the positive exponent.
For example, if we have a number, x, raised to the power of -n (x^(-n)), it can be rewritten as 1 / (x^n).
So, to determine whether the value is negative, we need to evaluate whether the reciprocal of the number raised to a positive exponent is positive or negative.
Now, let's consider the choices given:
a. always: This option is incorrect. A number raised to a negative exponent is not always negative. It depends on the value of the number itself.
b. never: This option is incorrect as well. A number raised to a negative exponent can indeed result in a negative value in certain cases.
c. sometimes: This option is correct. A number raised to a negative exponent is sometimes negative, depending on the value of the number. If the number is negative, then the resulting value will be negative. However, if the number is positive, the resulting value will be positive.
Therefore, the correct answer is c. sometimes.