Tell whether the each statement is sometimes, always or never true
1) If n is zero then x^-n is 1
2) If n is negative integer then x^-n=1
3) If x is zero then x^-n is 1
4) If n is an integer then x^-n>1
1 sometimes 0^0 is undefined
2 never
3 never
4 sometimes .3^1 < 1
Tell whether the statement is always, sometimes or never true.
Nine Students choose integers. seven of them are -16, 12, -13, -6, -5, 6 an 1
To determine whether each statement is sometimes, always, or never true, let's consider the given conditions.
1) If n is zero, then x^-n is 1:
This statement is always true. When n is zero, any nonzero number raised to the power of zero is equal to 1.
2) If n is a negative integer, then x^-n = 1:
This statement is never true. When n is a negative integer, x^-n is equal to 1 divided by x^n, which is not equal to 1 unless x is 1.
3) If x is zero, then x^-n is 1:
This statement is sometimes true. When x is zero, and n is any positive integer, x^-n is undefined because division by zero is undefined. However, when n is zero, x^-n is 1, as explained in statement 1.
4) If n is an integer, then x^-n > 1:
This statement is never true. If n is a nonzero integer, then x^-n is equal to 1 divided by x^n. Since dividing by a nonzero number decreases the value, x^-n is less than 1 unless x is 1.
In summary:
1) Sometimes True
2) Never True
3) Sometimes True
4) Never True