Question

Is the following statement true or false? If n is a negative integer, n^n = -1.

1. True
2. False

Answer 1

`{( - 2)}^( - 2) = \frac{1}{ {( - 2)}^(2) } = (1)/(4)`

The correct answer is #2 (False).

Answer 2

The statement "If n is a negative integer, n^n = -1" is false because the result of raising a negative integer to its own power varies and is not consistently -1.

Step-by-step explanation:

The statement "If n is a negative integer, n^n = -1" is false. When we raise a negative integer to a power, the result depends on whether the exponent is odd or even. If the exponent is odd, the result will indeed be negative, and if the exponent is even, the result will be positive. However, the statement that n^n will equal -1 for any negative integer n is not correct as the value is not consistently -1 for every negative integer raised to its own power.