Questions: For problems 17-20, indicate whether each result is a positive or a negative number 17. (-3)^2 18. (-4)^3 19. (-5)^(odd number) 20. (-6)^(even number) 21. The product (-1)^3 * (-1)^n is negative. Which of the following values of n Choose all that apply.

Solution Steps

To determine whether the result of each expression is positive or negative, consider the properties of exponents. For an expression of the form \((-a)^n\), if \(n\) is even, the result is positive, and if \(n\) is odd, the result is negative.

17. \((-3)^2\): Since the exponent is even, the result is positive.
18. \((-4)^3\): Since the exponent is odd, the result is negative.
19. \((-5)^{\text{odd number}}\): Since the exponent is odd, the result is negative.

The expression \((-3)^2\) involves squaring a negative number. Since the exponent is even, the result is positive. Mathematically, \((-3)^2 = 9\).

The expression \((-4)^3\) involves raising a negative number to an odd power. Since the exponent is odd, the result is negative. Mathematically, \((-4)^3 = -64\).

The expression \((-5)^{\text{odd number}}\) involves raising a negative number to an odd power. Since the exponent is odd, the result is negative. For example, \((-5)^3 = -125\).

Final Answer