Determine whether x to the third power is always, sometimes, or never a positive number for x+ ). Explain your reasoning.
To determine whether x to the third power is always, sometimes, or never a positive number for any value of x, we need to consider the properties of exponents and the behavior of the function.
The exponent of 3 means that we are multiplying the base x by itself three times. Since multiplication of two positive numbers always results in a positive number, we know that if x is positive, x to the third power will also be positive.
Now, let's consider the case where x is negative. When we multiply two negative numbers, we get a positive result. So, if x is negative, multiplying it by itself three times (x * x * x) will give us a positive number. Therefore, x to the third power is also positive when x is negative.
To summarize, x to the third power is always a positive number, regardless of whether x is positive or negative. Therefore, x to the third power is always positive and never negative or zero.